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A Complete Resource Book in Physics for JEE Main

Sanjeev Kumar

Chapter 1

Unit and Dimension - all with Video Answers

Educators

Chapter Questions

01:42

Problem 1

If we change unit of a physical quantity then
(A) its dimension changes.
(B) its dimension remain same.
(C) it may change or may not change.
(D) its magnitude changes.

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00:47

Problem 2

The least count of a stop watch is $1 / 5 \mathrm{~s}$. The time of 20 oscillations of a pendulum is measured to be $25 \mathrm{~s}$. The minimum percentage error in the measurement of time will be
(A) $0.1 \%$
(B) $0.8 \%$
(C) $1.8 \%$
(D) $8 \%$

Khoobchandra Agrawal
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03:12

Problem 3

Energy due to position of a particle is given by, $U=\frac{\alpha \sqrt{y}}{y+\beta}$, where $\alpha$ and $\beta$ are constants, $y$ is distance. The dimensions of $(\alpha \times \beta)$ are
(A) $\left[M^{0} L T^{0}\right]$
(B) $\left[M^{1 / 2} L^{3 / 2} T^{-2}\right]$
(C) $\left[M^{0} L^{-7 / 2} T^{0}\right]$
(D) $\left[M L^{7 / 2} T^{-2}\right]$

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01:45

Problem 4

A wire is of mass $(0.3 \pm 0.003) \mathrm{gm}$. The radius is $(0.5 \pm 0.005) \mathrm{mm}$ and length is $(6.0 \pm 0.06) \mathrm{cm}$ then
$\%$ error in density is
(A) 3
(B) 4
(C) 6
(D) $-2$

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01:55

Problem 5

The equation of state of some gases can be expressed as $\left(P+\frac{a}{V^{2}}\right)(V-b)=R T .$ Here, $P$ is the pressure, $V$ the volume, $T$ the absolute temperature, and $a, b, R$ are constants. The dimensions of $a$ are
(A) $\left[M L^{5} T^{-2}\right]$
(B) $\left[M L^{-1} T^{-2}\right]$
(C) $\left[M^{0} L^{3} T^{0}\right]$
(D) $\left[M^{0} L^{6} T^{0}\right]$

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01:12

Problem 6

We have error in the measurement of length, radius, mass and current of a wire are $2 \%, 3 \%, 2 \%$ and $1 \%$ then error in its density will be
(A) $11 \%$
(B) $8 \%$
(C) $10 \%$
(D) $7 \%$

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01:36

Problem 7

A physical quantity $x$ depends on qualities $y$ and $z$ as follows: $x=A y+B \tan C z$, where $A, B$ and $C$ are constants. Which of the following do not have the same dimensions?
(A) $x$ and $B$
(B) $C$ and $z^{-1}$
(C) $y$ and $B / A$
(D) $x$ and $A$

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02:00

Problem 8

The force $F$ is given in terms of time $t$ and displacement $x$ by the equation $F=A \cos B x+C \sin D t$. The dimensions of $\frac{D}{B}$ are
(A) $M^{0} L^{0} T^{0}$
(B) $M^{0} L^{0} T^{-1}$
(C) $M^{0} L^{-1} T^{0}$
(D) $M^{0} L^{1} T^{-1}$

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00:53

Problem 9

The diameter of a wire is measured with a screw gauge having 50 divisions on circular scale and by one complete rotation of circular scale, main scale moves $0.5 \mathrm{~mm}$. If reading of screw gauge is $0.250 \mathrm{~cm}$. The minimum percentage error in the reading will be
(A) $0.4$
(B) $0.8$
(C) 4
(D) 5

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01:42

Problem 10

The length, width and thickness of a block are (100.0 $\pm 0.1) \mathrm{cm},(10.00 \pm 0.01) \mathrm{cm}$ and $(1.000 \pm 0.001) \mathrm{cm}$
respectively. The maximum possible error in its volume will be
(A) $\pm 0.111 \mathrm{~cm}^{3}$
(B) $\pm 0.012 \mathrm{~cm}^{3}$
(C) $+0.03 \mathrm{~cm}^{3}$
(D) None of these

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02:19

Problem 11

The dimensional formula of magnetic flux is
(A) $\left[M L^{2} T^{-2} A^{-1}\right]$
(B) $\left[M L^{0} T^{-2} A^{-2}\right]$
(C) $\left[M^{0} L^{-2} T^{-2} A^{-2}\right]$
(D) $\left[M L^{2} T^{-1} A^{3}\right]$

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01:02

Problem 12

Error in the measurement of radius of sphere is $2 \%$. Then error in the calculation of volume will be
(A) $1 \%$
(B) $5 \%$
(C) $3 \%$
(D) $6 \%$

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02:25

Problem 13

The velocity of water waves may depend on their wavelength $\lambda$, the density of water $\rho$ and the acceleration due to gravity $g$. The method of dimensions gives the relation between these quantities as
(A) $v^{2} \propto \lambda g^{-1} \rho^{-1}$
(B) $v^{2} \propto g \lambda$
(C) $v^{2} \propto \lambda g \rho$
(D) $v^{2} \propto g^{-1} \lambda^{2}$

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02:37

Problem 14

A dust particle oscillates in air with a time period which depends on atmospheric pressure $P$, density of air $d$ and energy of the particle $E$, then time period is proportional to
(A)
$\begin{array}{ll}P^{-\frac{5}{6}} d^{\frac{1}{2}} E^{\frac{1}{3}} & \text { (B) } P^{\frac{1}{2}} d^{3} E^{-2}\end{array}$
(C)
$\begin{array}{ll}P^{-\frac{1}{3}} d^{\frac{1}{2}} E^{2} & \text { (D) } P^{-2} d^{-\frac{1}{2}} E^{-3}\end{array}$

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01:16

Problem 15

Which of the following group have different dimension?
(A) Potential difference, EMF, voltage
(B) Pressure, stress, Young's modulus
(C) Heat, energy, work-done
(D) Dipole moment, electric-flux, electric field

Pankaj Jain
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02:44

Problem 16

If a copper wire is stretched to make its radius decrease by $0.1 \%$, then the percentage increase in resistance is approximately
(A) $0.1 \%$
(B) $0.2 \%$
(C) $0.4 \%$
(D) $0.8 \%$

Sachin Rao
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02:22

Problem 17

Two resistances of $400 \Omega$ and $800 \Omega$ connected in series with a 6 volt battery of negligible internal resistance. A voltmeter of resistance $10,000 \Omega$ is used to measure the potential difference across $400 \Omega$. The error in the measurement of potential difference in volts approximately is
(A) $0.01$
(B) $0.02$
(C) $0.04$
(D) $0.05$

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01:24

Problem 18

If there is a positive error of $50 \%$ in the measurement of velocity of a body, then the error in the measurement of kinetic energy is
(A) $25_{-} \%$
(B) $50 \%$
(C) $100 \%$
(D) $125 \%$

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01:43

Problem 19

The pitch of a screw gauge is $1 \mathrm{~mm}$ and there are 100 divisions on its circular scale. When nothing is put in between its jaws, the zero of the circular scale lies 4 divisions below the reference line. When a steel wire is placed between the jaws, two main scale divisions are clearly visible and 67 divisions on the circular scale are observed. The diameter of the wire is
(A) $2.71 \mathrm{~mm}$
(B) $2.67 \mathrm{~mm}$
(C) $2.63 \mathrm{~mm}$
(D) $2.65 \mathrm{~mm}$

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02:33

Problem 20

Charge on the capacitor is given by $Q=I \alpha e^{-\frac{t}{\Delta V \varepsilon_{0} \beta}}$, where $\alpha$ and $\beta$ are constant, $t=$ time, $I=$ current, $\Delta V=$ Potential difference then, dimension of $\frac{\beta}{\alpha}$ is same as dimension of
(A) $\frac{1}{\sqrt{\mu_{0} \varepsilon_{0}}}$
(B) $\mu_{0} \varepsilon_{0}$
(C) $\frac{\mu_{0}}{\varepsilon_{0}}$
(D) $\frac{1}{\mu_{0} \varepsilon_{0}}$

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03:56

Problem 21

If the speed of light $(c)$, acceleration due to gravity $(g)$ and pressure $(p)$ are taken as fundamental units, the dimensional formula of gravitational constant $(G)$ will be
(A) $c^{0} g p^{-3}$
(B) $c^{2} g^{3} p^{-2}$
(C) $c^{0} g^{2} p^{-1}$
(D) $c^{2} g^{2} p^{-2}$

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02:46

Problem 22

The dimensions of $\frac{1}{\sqrt{\mu_{0} \varepsilon_{0}}}$ are
(A) $\left[I^{0} M^{0} L^{1} T^{-1}\right]$
(B) $\left[I^{2} M^{4} L^{-3} T^{1}\right]$
(C) $\left[I^{-2} T^{-2} L^{1} M^{1}\right]$
(D) $\left[I^{0} M^{0} L^{-1} T^{1}\right]$

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01:56

Problem 23

What are the dimensions of electrical permittivity?
(A) $M L^{-2} T^{-2} Q^{-2}$
(B) $M^{-1} L^{2} T^{-3} Q^{-1}$
(C) $M^{-1} L^{-3} T^{2} Q^{2}$
(D) $M^{-1} L^{3} T^{-2} Q^{-2}$

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01:38

Problem 24

The torque of force $\vec{F}=(2 \hat{i}-3 \hat{j}+4 \hat{k})$ newton acting at the point $\vec{r}=(3 \hat{i}+2 \hat{j}+3 \hat{k})$ metre about origin is (in $\mathrm{N}-\mathrm{m}$ )
(A) $6 \hat{i}-6 \hat{j}+12 \hat{k}$
(B) $17 \hat{i}-6 \hat{j}-13 \hat{k}$
(C) $-6 \hat{i}+6 \hat{j}-12 \hat{k}$
(D) $-17 \hat{i}+6 \hat{j}+13 \hat{k}$

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01:17

Problem 25

If a unit vector is represented by $0.5 \hat{i}+0.8 \hat{j}+c \hat{k}$ the value of $c$ is
(A) 1
(B) $\sqrt{0.11}$
(C) $\sqrt{0.01}$
(D) $0.39$

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01:23

Problem 26

The vector sum of two forces is perpendicular to their vector differences. In that case, the forces
(A) are not equal to each other in magnitude.
(B) cannot be predicted.
(C) are equal to each other.
(D) are equal to each other in magnitude.

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01:40

Problem 27

Two vectors $\vec{A}$ and $\vec{B}$ are such that $\vec{A}+\vec{B}=\vec{C}$ and $A^{2}+B^{2}=C^{2}$
If $\theta$ is the angle between positive direction of $\vec{A}$ and $\vec{B}$ then the correct statement is (B) $\theta=\frac{2 \pi}{3}$
(A) $\theta=\pi$
(C) $\theta=0$
(D) $\theta=\frac{\pi}{2}$

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03:27

Problem 28

Given that $\vec{P}+\vec{Q}+\vec{R}=0$. Two out of the three vectors are equal in magnitude. The magnitude of the third vector is $\sqrt{2}$ times that of the other two. Which of the following can be the angles between these vectors?
(A) $90^{\circ}, 135^{\circ}, 135^{\circ}$
(B) $45^{\circ}, 45^{\circ}, 90^{\circ}$
(C) $30^{\circ}, 60^{\circ}, 90^{\circ}$
(D) $45^{\circ}, 90^{\circ}, 135^{\circ}$

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02:12

Problem 29

The angle between $\vec{P}+\vec{Q}$ and $\vec{P}-\vec{Q}$ will be
(A) $90^{\circ}$
(B) Between $0^{\circ}$ and $180^{\circ}$
(C) $180^{\circ}$ only
(D) None of these

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01:31

Problem 30

If the vectors $\vec{P}=a \hat{i}+a \hat{j}+3 \hat{k}$ and $\vec{Q}=a \hat{i}-2 \hat{j}-\hat{k}$
are perpendicular to each other, then the positive value of a is
(A) Zero
(B) 1
(B) 2
(D) 3

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01:55

Problem 31

The angles which the vector $\vec{A}=3 \hat{i}+6 \hat{j}+2 \hat{k}$ makes with the co-ordinate axes are
(A) $\cos ^{-1} \frac{3}{7}, \cos ^{-1} \frac{6}{7}$ and $\cos ^{-1} \frac{2}{7}$
(B) $\cos ^{-1} \frac{4}{7}, \cos ^{-1} \frac{5}{7}$ and $\cos ^{-1} \frac{3}{7}$
(C) $\cos ^{-1} \frac{3}{7}, \cos ^{-1} \frac{4}{7}$ and $\cos ^{-1} \frac{1}{7}$
(D) None of the above

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01:25

Problem 32

Unit vector parallel to the resultant of vectors $\vec{A}=4 \hat{i}-3 \hat{j}$ and $\vec{B}=8 \hat{i}+8 \hat{j}$ will be
(A) $\frac{24 \hat{i}+5 \hat{j}}{13}$
(B) $\frac{12 \hat{i}+5 \hat{j}}{13}$
(C) $\frac{6 \hat{i}+5 \hat{j}}{13}$
(D) None of these

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01:29

Problem 33

The value of $n$ so that vectors $2 \hat{i}+3 \hat{j}-2 \hat{k}, 5 \hat{i}+n \hat{j}+\hat{k}$ and $-\hat{i}+2 \hat{j}+3 \hat{k}$ may be coplanar, will be
(A) 18
(B) 28
(C) 9
(D) 36

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02:57

Problem 34

If $\vec{a}$ and $\vec{b}$ are two vectors then the value of $(\vec{a}+\vec{b}) \times(\vec{a}-\vec{b})$ is
(A) $2(\vec{b} \times \vec{a})$
(B) $-2(\vec{b} \times \vec{a})$
(C) $\vec{b} \times \vec{a}$
(D) $\vec{a} \times \vec{b}$

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01:24

Problem 35

The component of vector $\vec{A}=2 \hat{i}+3 \hat{j}$ along the vector $\hat{i}+\hat{j}$ is
(A) $\frac{5}{\sqrt{2}}$
(B) $10 \sqrt{2}$
(C) $5 \sqrt{2}$
(D) 5

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02:00

Problem 36

Three vectors satisfy the relation $\vec{A} \cdot \vec{B}=0$ and $\vec{A} \cdot \vec{C}=0$, then $\vec{A}$ is parallel to
(A) $\vec{C}$
(B) $\vec{B}$
(C) $\vec{B} \times \vec{C}$
(D) $\vec{B} \cdot \vec{C}$

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02:19

Problem 37

If $|\vec{A} \times \vec{B}|=\sqrt{3} \vec{A} \cdot \vec{B}$, then the value of $|\vec{A}+\vec{B}|$ is
(A) $\left(A^{2}+B^{2}+A B\right)^{1 / 2}$
(B) $\left(A^{2}+B^{2}+\frac{A B}{\sqrt{3}}\right)^{1 / 2}$
(C) $(A+B)$
(D) $\left(A^{2}+B^{2}+\sqrt{3} A B\right)^{1 / 2}$

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01:53

Problem 38

If the angle between the vectors $\vec{A}$ and $\vec{B}$ is $\theta$, the value of the product $(\vec{B} \times \vec{A}) \cdot \vec{A}$ is equal to
(A) $B A^{2} \cos \theta$
(B) $B A^{2} \sin \theta$
(C) $B A^{2} \sin \theta \cos \theta$
(D) Zero

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01:37

Problem 39

The $(x, y, z)$ co-ordinates of two points $A$ and $B$ are given respectively as $(0,3,-1)$ and $(-2,6,4)$. The displacement vector from $A$ to $B$ is given by
(A) $-2 \hat{i}+6 \hat{j}+4 \hat{k}$
(B) $-2 \hat{i}+3 \hat{j}+3 \hat{k}$
(C) $-2 \hat{i}+3 \hat{j}+5 \hat{k}$
(D) $2 \hat{i}-3 \hat{j}-5 \hat{k}$

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01:46

Problem 40

Calculate the area of the triangle determined by the two vectors $\vec{A}=3 \hat{i}+4 \hat{j}$ and $\vec{B}=-3 \hat{i}+7 \hat{j}$
(A) $\frac{33}{2}$ sq. unit
(B) $\frac{35}{2} \mathrm{sq}$. unit
(C) $\frac{45}{2}$ sq. unit
(D) 15 sq. unit

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02:01

Problem 41

Determine that vector which when added to the resultant of $\vec{A}=3 \hat{i}-5 \hat{j}+7 \hat{k}$ and $\vec{B}=2 \hat{i}+4 \hat{j}-3 \hat{k}$ gives a
unit vector along the $y$-direction.
(A) $5 \hat{i}+2 \hat{j}-4 \hat{k}$
(B) $-5 \hat{i}+2 \hat{j}-4 \hat{k}$
(C) $5 \hat{i}-2 \hat{j}-4 \hat{k}$
(D) None of these

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02:15

Problem 42

The vectors $\vec{A}=3 \hat{i}-2 \hat{j}+\hat{k}, \vec{B}=\hat{i}-3 \hat{j}+5 \hat{k}$ and $\vec{C}=$
$2 \hat{i}+\hat{j}-4 \hat{k}$ form a triangle, then the triangle is
(A) right angled triangle
(B) lateral triangle
(C) isolated triangle
(D) None of these

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02:17

Problem 43

From Fig. $1.24$, the correct relation is
(A) $\vec{A}+\vec{B}+\vec{E}=\overrightarrow{0}$
(B) $\vec{C}-\vec{D}=-\vec{A}$
(C) $\vec{B}+\vec{E}-\vec{C}=-\vec{D}$
(D) All of the above

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02:35

Problem 44

The ratio of maximum and minimum magnitudes of the resultant of two vectors $\vec{a}$ and $\vec{b}$ is $3: 1$. Now $|\vec{a}|$ is equal to
(A) $|\vec{b}|$
(B) $2|\vec{b}|$
(C) $3|\vec{b}|$
(D) $4|\vec{b}|$

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01:14

Problem 45

The projection of a vector $\vec{r}=3 \hat{i}+\hat{j}+2 \hat{k}$ on the $x-y$ plane has magnitude
(A) 3
(B) 4
(C) $\sqrt{14}$
(D) $\sqrt{10}$

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01:19

Problem 46

If $|\vec{A}+\vec{B}|=|\vec{A}|=|\vec{B}|$, then the angle between $\vec{A}$ and $\vec{B}$ is
(A) $120^{\circ}$
(B) $60^{\circ}$
(C) $90^{\circ}$
(D) $0^{\circ}$

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02:36

Problem 47

Given $\left|\overrightarrow{A_{1}}\right|=2,\left|\overrightarrow{A_{2}}\right|=3$ and $\left|\overrightarrow{A_{1}}+\overrightarrow{A_{2}}\right|=3$. Find the
value of $\left(\overrightarrow{A_{1}}+2 \overrightarrow{A_{2}}\right) \cdot\left(3 \overrightarrow{A_{1}}-4 \overrightarrow{A_{2}}\right)$
(A) $-64$
(B) 60
(C) $-60$
(D) 64

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02:03

Problem 48

In going from one city to another, a car travels $75 \mathrm{~km}$ north, $60 \mathrm{~km}$ north-west and $20 \mathrm{~km}$ east. The magnitude of displacement between the two cities is (take $1 \sqrt{2}=0.7)$
(A) $170 \mathrm{~km}$
(B) $137 \mathrm{~km}$
(C) $119 \mathrm{~km}$
(D) $140 \mathrm{~km}$

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01:48

Problem 49

Given $\vec{A}=2 \hat{i}+p \hat{j}+q \hat{k}$ and $\vec{B}=5 \hat{i}+7 \hat{j}+3 \hat{k}$. If $\vec{A} \| \vec{B}$
then the values of $p$ and $q$ are, respectively,
(A) $\frac{14}{5}$ and $\frac{6}{5}$
(B) $\frac{14}{3}$ and $\frac{6}{5}$
(C) $\frac{6}{5}$ and $\frac{1}{3}$
(D) $\frac{3}{4}$ and $\frac{1}{4}$

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02:09

Problem 50

If $\vec{b}=3 \hat{i}+4 \hat{j}$ and $\vec{a}=\hat{i}-\hat{j}$, the vector having the same magnitude as that of $\vec{b}$ and parallel to $\vec{a}$ is
(A) $\frac{5}{\sqrt{2}}(\hat{i}-\hat{j})$
(B) $\frac{5}{\sqrt{2}}(\hat{i}+\hat{j})$
(C) $5(\hat{i}-\hat{j})$
(D) $5(\hat{i}+\hat{j})$

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02:02

Problem 51

Mark the correct statement
(A) $|\vec{a}+\vec{b}| \geq|\vec{a}|+|\vec{b}|$
(B) $|\vec{a}+\vec{b}| \leq|\vec{a}|+|\vec{b}|$
(C) $|\vec{a}-\vec{b}| \geq|\vec{a}|+|\vec{b}|$
(D) All of the above

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03:04

Problem 52

Two forces $\vec{F}_{2}=500 \mathrm{~N}$ due east and $\vec{F}_{2}=250 \mathrm{~N}$ due north have their common initial point. $\vec{F}_{2}-\vec{F}_{1}$ is
(A) $250 \sqrt{5} \mathrm{~N}, \tan ^{-1}(2) \mathrm{W}$ of $\mathrm{N}$
(B) $250 \mathrm{~N}, \tan ^{-1}(2) \mathrm{W}$ of $\mathrm{N}$
(C) Zero
(D) $750 \mathrm{~N}, \tan ^{-1}(3 / 4) \mathrm{N}$ of $\mathrm{W}$

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01:49

Problem 53

In a two-dimensional motion of a particle, the particle moves from point $A$, with position vector $\vec{r}_{1}$, to point $B$, with position vector $\vec{r}_{2}$. If the magnitudes of these vectors are, respectively, $r_{1}=3$ and $r_{2}=4$ and the angles they make with the $x$-axis are $\theta_{1}=75^{\circ}$ and $\theta_{2}=15^{\circ}$, respectively, then find the magnitude of the displacement vector.
(A) 15
(B) $\sqrt{13}$
(C) 17
(D) $\sqrt{15}$

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02:56

Problem 54

Which of the following having same dimension?
(A) Electric flux, electric field, electric dipole moment
(B) Pressure, stress, young's modulus
(C) Electromotive force, potential difference, electric voltage
(D) Heat, potential energy, work done.

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01:42

Problem 55

The ratio of the dimension of Planck's constant and that of moment of inertia is the dimension of
(A) Time
(B) Frequency
(C) Angular momentum
(D) Velocity

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01:16

Problem 56

Out of the following pairs, which one does not have the same dimensions?
(A) Angular momentum and Planck's constant.
(B) Impulse and momentum.
(C) Moment of inertia and moment of force.
(D) Work and torque.

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01:21

Problem 57

Parsec is the unit of
(A) Time
(B) Distance
(C) Frequency
(D) Angular acceleration

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01:29

Problem 58

(A) Specific gravity of a fluid is a dimensionless quantity $(R)$. It is the ratio of density of fluid to density of water.
(A) Both $A$ and $R$ are correct and $R$ is the correct explanation of $A$
(B) Both $A$ and $R$ are correct but $R$ is not the correct explanation of $A$
(C) $A$ is correct but $R$ is false
(D) Both $A$ and $R$ are false

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01:35

Problem 59

A force $F$ is given by $F=a t+b t^{2}$ where $t$ is time, what are the dimension of $a$ and $b ?$
(A) $\left[M L T^{-1}, M L T^{0}\right]$,
(B) $\left[M L T^{-3}, M L^{2} T^{4}\right]$
(C) $\left[M L T^{-4}, M L T^{-1}\right]$
(D) $\left[M L^{-3} T, M L T^{-4}\right]$

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Numerade Educator
01:55

Problem 60

Which of the following is not a unit of Young's modulus?
(A) $\mathrm{Nm}^{-1}$
(B) $\mathrm{Nm}^{-2}$
(C) Dyne $\mathrm{cm}^{-2}$
(D) Mega pascal

Akshaya Rs
Akshaya Rs
Numerade Educator
01:30

Problem 61

If $M$ is mass of the earth and $R$ its radius, the ratio of the gravitational acceleration and the gravitational constant is
(A) $\frac{R^{2}}{M}$
(B) $\frac{M}{R^{2}}$
(C) $M R^{2}$
(D) $\frac{M}{R}$

Akshaya Rs
Akshaya Rs
Numerade Educator
01:58

Problem 62

A hypothetical experiment conducted to find Young's modulus $Y=\frac{\cos \theta T^{x} \tau}{l^{3}}$ where $\tau$ is torque and $l$ is length then find $x$.
(A) 0
(B) 1
(C) 2
(D) 3

Akshaya Rs
Akshaya Rs
Numerade Educator
02:40

Problem 63

Find the dimensions of $\frac{B^{2}}{\mu_{o}}$
(A) $M L^{2} T^{-2}$
(B) $M L^{-1} T^{-1}$
(C) $M L^{-2} T^{-2}$
(D) $M L^{-1} T^{-2}$

Akshaya Rs
Akshaya Rs
Numerade Educator
02:01

Problem 64

While printing a book a printer made certain mistakes in the following relation. Find the correct relation.
(A) $y=A \sin \omega \theta$
(B) $y=A \sin (\omega x+\theta)$
(C) $y=A \sin (\omega t+\theta) x$
(D) $y=\frac{A}{-} \sin \omega t+\theta$

Akshaya Rs
Akshaya Rs
Numerade Educator
01:38

Problem 65

The velocity of surface waves depends upon surface tension, coefficient of viscosity and density. The relation is
(A) $\frac{s^{2}}{\rho \eta}$
(B) $\frac{s}{\eta}$
(C) $\frac{\eta \rho}{s^{2}}$
(D) $\frac{\rho}{\eta}$

Akshaya Rs
Akshaya Rs
Numerade Educator
00:52

Problem 66

Which of the following pair has different dimensions?
(A) Electric pressure, energy density
(B) Intensity, $\in_{o} E_{o}^{2} c$
(C) Reynold's number and time constant
(D) Work, Torque

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:44

Problem 67

A chocolate cookie is a circular disk of diameter $8.50$ $\pm 0.02 \mathrm{~cm}$ and thickness $0.050 \pm 0.005 \mathrm{~cm}$. The average volume in $\mathrm{cm}^{3}$ is
(A) $2.83 \pm 0.3$
(B) $2.38 \pm 0.27$
(C) $11.35 \pm 1.2$
(D) $9.31 \pm 1.12$

Akshaya Rs
Akshaya Rs
Numerade Educator
01:52

Problem 68

The fastest commercial airline service is $1450 \mathrm{mi} / \mathrm{h}$. Find the speed in $\mathrm{kmh}^{-1}$ and $\mathrm{ms}^{-1}$.
(A) $1938 \mathrm{kmh}^{-1}, 618.3 \mathrm{~ms}^{-1}$
(B) $2030 \mathrm{kmh}^{-1}, 623.1 \mathrm{~ms}^{-1}$
(C) $2334 \mathrm{kmh}^{-1}, 647.5 \mathrm{~ms}^{-1}$
(D) None

Akshaya Rs
Akshaya Rs
Numerade Educator
02:35

Problem 69

Two capacitors $C_{1}=5.2 \mu F$ and $0.1 \mu F$ and $c_{2}=12.2 \mu F$ are joined (i) In series (ii) In parallel. Find the net capacitance in these two cases.
(A) $2.8 \%, 1.23 \%$
(B) $3.6 \%, 1.31 \%$
(C) $3.4 \%, 1.3 \%$
(D) $3.9 \%, 1.15 \%$

Akshaya Rs
Akshaya Rs
Numerade Educator
01:18

Problem 70

$V^{-1}$ stands for
(A) electric flux.
(B) electric pressure.
(C) electric field density.
(D) capacitance.

Akshaya Rs
Akshaya Rs
Numerade Educator
01:50

Problem 71

A spherometer has 20 threads per $\mathrm{cm}$. Its circular scale has 100 divisions. Find the least count of spherometer.
(A) $5 \mu \mathrm{m}$
(B) $50 \mu \mathrm{m}$
(C) $0.5 \mu \mathrm{m}$
(D) $0.5 \mu \mathrm{m}$

Akshaya Rs
Akshaya Rs
Numerade Educator
02:54

Problem 72

Which of the following are dimensionally correct?
(A) $h=\frac{2 T \cos \theta}{\rho r g}$
(B) $v=\sqrt{\frac{p}{\rho}}$
(C) $\frac{d v}{d t}=\frac{\pi p r^{4} t}{\delta \eta l}$
(D) $T=\sqrt{\frac{m g l}{I}}$

Akshaya Rs
Akshaya Rs
Numerade Educator
01:52

Problem 73

$\int \frac{d x}{\sqrt{a^{2}-x^{2}}}=\frac{1}{a} \sin ^{-1} \frac{a}{x}$
(A) is dimensionally correct.
(B) dimensionally incorrect.
(C) such mathematical relations cannot be tested.
(D) cannot say.

Akshaya Rs
Akshaya Rs
Numerade Educator
01:52

Problem 74

In $\mathrm{CH}_{4}$ molecule, there are four $\mathrm{C}-\mathrm{H}$ bonds. If two adjacent bonds are in $\hat{i}+\hat{j}+\hat{k}$ and $\hat{i}-\hat{j}-\hat{k}$ direction, then find the angle between these bonds.
(A) $\sin ^{-1}\left(\frac{-1}{3}\right)$
(B) $\cos ^{-1}\left(\frac{1}{3}\right)$
(C) $\sin ^{-1}\left(\frac{1}{3}\right)$
(D) $\cos ^{-1}\left(\frac{-1}{3}\right)$

Akshaya Rs
Akshaya Rs
Numerade Educator
02:01

Problem 75

Two vectors $\vec{A}$ and $\vec{B}$ have magnitude 3 each. $\vec{A} \times \vec{B}=-5 \hat{k}+2 \hat{i}$. Find angle between $A$ and $B$
(A) $\cos ^{-1} \frac{\sqrt{29}}{9}$
(B) $\tan ^{-1}\left(\frac{-5}{2}\right)$
(C) $\sin ^{-1}\left(\frac{2}{5}\right)$
(D) $\sin ^{-1}\left(\frac{\sqrt{29}}{9}\right)$

Akshaya Rs
Akshaya Rs
Numerade Educator
01:46

Problem 76

A particle moving eastwards with $5 \mathrm{~m} / \mathrm{s}^{-1}$. In $10 \mathrm{~s}$ the velocity changes to $5 \mathrm{~m} / \mathrm{s}^{-1}$ northwards. The average acceleration in this time is
(A) $\frac{1}{\sqrt{2}} \mathrm{~m} / \mathrm{s}^{-2}$ towards Northeast
(B) $\frac{1}{2} \mathrm{~m} / \mathrm{s}^{-2}$ towards North
(C) $\frac{1}{\sqrt{2}} \mathrm{~m} / \mathrm{s}^{-2}$ towards Northwest
(D) Zero

Akshaya Rs
Akshaya Rs
Numerade Educator
01:22

Problem 77

If a vector $2 \hat{i}+3 \hat{j}+8 \hat{k}$ is perpendicular to the vector $4 \hat{j}-4 \hat{i}+\alpha \hat{k}$ then the value of $\alpha$ is
(A) $\frac{1}{2}$
(B) $\frac{-1}{2}$
(C) 1
(D) $-1$

Akshaya Rs
Akshaya Rs
Numerade Educator
01:44

Problem 78

If the angle between the vectors $\vec{A}$ and $\vec{B}$ is $\theta$, the value of the product. $(\vec{B} \times \vec{A}) \vec{A}$ equals
(A) $B A^{2} \sin \theta$
(B) $B A^{2} \cos \theta \sin \theta$
(C) $B A^{2} \cos \theta$
(D) Zero

Akshaya Rs
Akshaya Rs
Numerade Educator
02:34

Problem 79

A river is flowing from $\mathrm{W}$ to $\mathrm{E}$ with a speed $5 \mathrm{~m} / \mathrm{min}$. A man can swim in still waters at a velocity $10 \mathrm{~m} / \mathrm{min}$. In which direction should a man swim to take the shortest path to reach the south bank?
(A) $30^{\circ}$ East of South
(B) $60^{\circ}$ East of North
(C) South
(D) $30^{\circ}$ West of North

Akshaya Rs
Akshaya Rs
Numerade Educator
01:47

Problem 80

Electrons in a TV tube move horizontally South to North. Vertical component of earth's magnetic field points down. The electron is deflected towards
(A) West
(B) No deflection
(C) East
(D) North to South

Akshaya Rs
Akshaya Rs
Numerade Educator
01:40

Problem 81

If $\vec{A} \cdot \vec{B}=\vec{B} \cdot \vec{C}$, then
(A) $\vec{A}=\vec{C}$ always
(B) $\vec{A} \neq \vec{C}$ always
(C) $\vec{A}$ may not be equal to $\vec{C}$
(D) None of these

Akshaya Rs
Akshaya Rs
Numerade Educator
01:58

Problem 82

$A=3 \hat{i}+4 \hat{j}$ find a vector perpendicular to $\vec{A}$ in the plane of $\vec{A}$
(A) $\hat{k}$
(B) $-3 \hat{i}-4 \hat{j}$
(C) $4 \hat{j}-3 \hat{i}$
(D) $4 \hat{i}-3 \hat{j}$

Akshaya Rs
Akshaya Rs
Numerade Educator
02:25

Problem 83

Find a vector $\vec{x}$ which is perpendicular to both $\vec{A}$ and $\vec{B}$ but has magnitude equal to that of $\vec{B}$. Rule: Inter change coeff. of $\hat{i}$ and $\hat{j}$ and change sign of one of the vectors.
$\vec{A}=3 \hat{i}-2 \hat{j}+\hat{k}, \vec{B}=4 \hat{i}+3 \hat{j}-2 \hat{k}$
(A) $\frac{1}{\sqrt{10}}(\hat{i}+10 \hat{j}+17 \hat{k})$
(B) $\frac{1}{\sqrt{10}}(\hat{i}-10 \hat{j}+17 \hat{k})$
(C) $\sqrt{\frac{29}{390}}(\hat{i}-10 \hat{j}+17 \hat{k})$
(D) $\sqrt{\frac{29}{390}}(\hat{i}+10 \hat{j}+17 \hat{k})$

Akshaya Rs
Akshaya Rs
Numerade Educator
01:46

Problem 84

Rain is falling vertically with $3 \mathrm{~ms}^{-1}$ and a man is moving due North with $4 \mathrm{~ms}^{-1}$. In which direction he should hold the umbrella to protect himself from rains?
(A) $37^{\circ}$ North of vertical
(B) $37^{\circ}$ South of vertical
(C) $53^{\circ}$ North of vertical
(D) $53^{\circ}$ South of vertical

Akshaya Rs
Akshaya Rs
Numerade Educator
01:48

Problem 85

A man is moving on his bike with $54 \mathrm{kmh}^{-1}$. He takes a u-turn in $10 \mathrm{~s}$ and continues to move with the some velocity. Find average acceleration during this time.
(A) $3.0 \mathrm{~ms}^{-2}$
(B) $1.5 \mathrm{~ms}^{-2}$
(C) 0
(D) $-1.5 \mathrm{~ms}^{-2}$

Akshaya Rs
Akshaya Rs
Numerade Educator
04:10

Problem 86

A man starts from $O$ moves $500 \mathrm{~m}$ turns by $60^{\circ}$ and moves $500 \mathrm{~m}$ again turns by $60^{\circ}$ and moves $500 \mathrm{~m}$ and so on. Find the displacement after (i) 5 th turn, (ii) 3 rd turn
(A) $500 \mathrm{~m}, 1000 \mathrm{~m}$
(B) $500 \mathrm{~m}, 500 \sqrt{3} \mathrm{~m}$
(C) $1000 \mathrm{~m}, 500 \sqrt{3} \mathrm{~m}$
(D) None of these

Akshaya Rs
Akshaya Rs
Numerade Educator
01:40

Problem 87

If $\vec{B}=\lambda \vec{A}$ then $\frac{\vec{B}}{\vec{A}}=\ldots$
(A) $\lambda$
(B) $\frac{1}{\lambda}$
(C) $\frac{\lambda}{2}$
(D) Indeterminate

Akshaya Rs
Akshaya Rs
Numerade Educator
02:15

Problem 88

The acceleration of a particle as seen from two frames $S_{1}$ and $S_{2}$ has equal magnitude $5 \mathrm{~ms}^{-2}$.
(A) The frames must be at rest with respect to each other.
(B) The frames may be moving with respect to each other but neither should be accelerated with respect to the other.
(C) The acceleration of frame $S_{2}$ with respect to $S_{1}$ be 0 or $10 \mathrm{~ms}^{-2}$
(D) The acceleration of $S_{2}$ with respect to $S_{1}$ lies between 0 and $10 \mathrm{~ms}^{-2}$.

Akshaya Rs
Akshaya Rs
Numerade Educator
03:59

Problem 89

A man running on a horizontal road at $8 \mathrm{~ms}^{-1}$ finds rain falling vertically. If he increases his speed to $12 \mathrm{~ms}^{-1}$, he finds that drops make $30^{\circ}$ angle with the vertical. Find velocity of rain with respect to the road.
(A) $4 \sqrt{7} \mathrm{~ms}^{-1}$
(B) $8 \sqrt{2} \mathrm{~ms}^{-1}$
(C) $7 \sqrt{3} \mathrm{~ms}^{-1}$
(D) $8 \mathrm{~ms}^{-1}$

Akshaya Rs
Akshaya Rs
Numerade Educator
01:51

Problem 90

In Fig. $1.25$ (A) shown find the velocity of block $m$ if both the rope ends are pulled with $a$ velocity $v$.
(A) $2 v \cos \theta$
(B) $\frac{v}{\cos \theta}$
(C) $\frac{v}{2 \cos \theta}$
(D) $\frac{2 v}{\cos \theta}$

Akshaya Rs
Akshaya Rs
Numerade Educator
01:27

Problem 91

Which of the following cannot be in equilibrium?
(A) $10 \mathrm{~N}, 10 \mathrm{~N}, 5 \mathrm{~N}$
(B) $5 \mathrm{~N}, 7 \mathrm{~N}, 9 \mathrm{~N}$
(C) $8 \mathrm{~N}, 4 \mathrm{~N}, 13 \mathrm{~N}$
(D) $9 \mathrm{~N}, 6 \mathrm{~N}, 5 \mathrm{~N}$

Akshaya Rs
Akshaya Rs
Numerade Educator
02:02

Problem 92

$\vec{A}=3 \hat{i}+4 \hat{j}+2 \hat{k}, \vec{B}=6 \hat{i}-\hat{j}+3 \hat{k}$. Find a vector paral-
lel to $\vec{A}$ whose magnitude is equal to that of $\vec{B}$.
(A) $\sqrt{\frac{46}{29}}(3 \hat{i}+4 \hat{j}+2 \hat{k})$
(B) $\sqrt{\frac{46}{29}}(6 \hat{i}-\hat{j}+3 \hat{k})$
(C) $\sqrt{\frac{29}{46}}(3 \hat{i}+4 \hat{j}+2 \hat{k})$
(D) None

Akshaya Rs
Akshaya Rs
Numerade Educator
01:50

Problem 93

$\vec{a}, \vec{b}, \vec{c}$ are three coplanar vectors. Find the vector sum. $\vec{a}=4 \hat{i}-\hat{j}, \vec{b}=-3 \hat{i}+2 \hat{j}, \vec{c}=-3 \hat{j}$
(A) $\sqrt{5}, 297^{\circ}$
(B) $\sqrt{5}, 63^{\circ}$
(C) $\sqrt{3}, 297^{\circ}$
(D) $\sqrt{3}, 63^{\circ}$

Akshaya Rs
Akshaya Rs
Numerade Educator
02:11

Problem 94

A block of mass $m$ is connected to three springs, each of spring constant $k$ as shown in Fig. $1.26 .$ The block is pulled by $x$ in the direction of $C$. Find resultant spring constant.
(A) $k$
(B) $2 k$
(C) $3 \mathrm{k}$
(D) $\frac{3 k}{2}$

Akshaya Rs
Akshaya Rs
Numerade Educator
01:53

Problem 95

A particle moves in the $x-y$ plane under the action of force $\vec{F}$ such that the value of its linear momentum 2 at any instant is $p=2(\cos t \hat{i}+\sin t \hat{j})$. The angle $\theta$
between $F$ and $p$ is
(A) $60^{\circ}$
(B) $45^{\circ}$
(C) $30^{\circ}$
(D) $90^{\circ}$

Akshaya Rs
Akshaya Rs
Numerade Educator
01:52

Problem 96

Consider a collection of large number of particles, each moving with a speed $v$. The direction of velocity is randomly distributed in the collection. The magnitude of the relative velocity between a pair of particles averaged over all the pairs in the collection
(A) $v$
(B) $\frac{2 v}{\pi}$
(C) $\frac{\pi v}{4}$
(D) $\frac{4 v}{\pi}$

Akshaya Rs
Akshaya Rs
Numerade Educator
01:59

Problem 97

A steamer is moving due east with $36 \mathrm{~km} / \mathrm{h}$. To a man in the steamer the wind appears to blow at $18 \mathrm{~km} / \mathrm{h}$ due north. Find the velocity of the wind.
(A) $5 \sqrt{5} \mathrm{~ms}^{-1} \tan ^{-1} \frac{1}{2}$ North of East
(B) $5 \mathrm{~ms}^{-1} \tan ^{-1} 2$ North of East
(C) $5 \sqrt{5} \mathrm{~ms}^{-1} \tan ^{-1} 2$ North of East
(D) $5 \mathrm{~ms}^{-1} \tan ^{-1} \frac{1}{2}$ North of East

Akshaya Rs
Akshaya Rs
Numerade Educator
01:59

Problem 98

The position vector of a particle is $\vec{r}=a[\cos \omega t \hat{i}+$ $\left.\sin \omega t^{-} j\right]$. The velocity of the particle is
(A) parallel to position vector.
(B) directed towards origin.
(C) directed away from origin.
(D) perpendicular to position vector.

Akshaya Rs
Akshaya Rs
Numerade Educator
01:34

Problem 99

A force $6 \hat{i}+3 \hat{j}+\hat{k}$ Newton displaces a particles from $A(0,3,2)$ to $B(5,1,6)$. Find the work done.
(A) $10 \mathrm{~J}$
(B) $22 \mathrm{~J}$
(C) $32 \mathrm{~J}$
(D) $\underline{41 J}$

Akshaya Rs
Akshaya Rs
Numerade Educator
02:00

Problem 100

Wind is blowing $\mathrm{NE}$ with $18 \sqrt{2} \mathrm{~km} \mathrm{~h}^{-1}$ and steamer is heading due west with $18 \mathrm{~km} \mathrm{~h}^{-1}$. In which direction is the flag on the mast fluttering?
(A) North West
(B) North
(C) South West
(D) South

Akshaya Rs
Akshaya Rs
Numerade Educator
01:28

Problem 101

The resultant of two forces equal in magnitude is equal to either of two vectors in magnitude. Find the angle between the forces.
(A) $60^{\circ}$
(B) $45^{\circ}$
(C) $90^{\circ}$
(D) $120^{\circ}$

Akshaya Rs
Akshaya Rs
Numerade Educator
01:43

Problem 102

A man goes $100 \mathrm{~m}$ north then $100 \mathrm{~m}$ east and then $20 \mathrm{~m}$ north and then $100 \sqrt{2} \mathrm{~m}$ south-West. Find the displacement.
(A) $20 \mathrm{~m}$ West
(B) $20 \mathrm{~m}$ East
(C) $20 \mathrm{~m}$ North
(D) $20 \mathrm{~m}$ South

Akshaya Rs
Akshaya Rs
Numerade Educator
01:40

Problem 103

If force, length and time are fundamental quantities, then find the dimensions of density is
(A) $\mathrm{FL}^{-4} \mathrm{~T}^{-2}$
(B) $\mathrm{FL}^{-4} \mathrm{~T}^{2}$
(C) $\mathrm{FL}^{-1} \mathrm{~T}^{-2}$
(D) $\mathrm{FL}^{-1} \mathrm{~T}^{2}$

Akshaya Rs
Akshaya Rs
Numerade Educator
01:08

Problem 104

Dimensions of $\frac{1}{\mu_{0} \varepsilon_{0}}$, where symbols have their usual meaning are $[\mathbf{2 0 0 3}]$
(A) $\left[L^{-1} T\right]$
(B) $\left[L^{2} T^{2}\right]$
(C) $\left[L^{2} T^{-2}\right]$
(D) $\left[L T^{-1}\right]$

Akshaya Rs
Akshaya Rs
Numerade Educator
02:25

Problem 105

The physical quantities not having same dimensions are =
(A) torque and work.
(B) momentum and Planck's constant.
(C) stress and Young's modulus.
(D) speed and $\left(\mu_{0} \varepsilon_{0}\right)^{-1 / 2}$.

Akshaya Rs
Akshaya Rs
Numerade Educator
01:14

Problem 106

Which one of the following represents the correct dimensions of the coefficient of viscosity?
(A) $\left[M L^{-1} T^{-2}\right]$
(B) $\left[M L T^{-1}\right]$
(C) $\left[M L^{-1} T^{-1}\right]$
(D) $\left[M L^{-2} T^{-2}\right]$

Akshaya Rs
Akshaya Rs
Numerade Educator
02:04

Problem 107

Which of the following units denotes the dimensions $\left[M L^{2} / Q^{2}\right]$, where $Q$ denotes the electric charge?
(A) $\mathrm{Wb} / \mathrm{m}^{2}$
(B) Henry (H)
(C) $\mathrm{H} / \mathrm{m}^{2}$
(D) Weber (Wb)

Akshaya Rs
Akshaya Rs
Numerade Educator
01:33

Problem 108

The dimensions of magnetic field in $M, L, T$ and $C$ (Coulomb) is given as
(A) $\left[M L T^{-1} C^{-1}\right]$
(B) $\left[M T^{2} C^{-2}\right]$
(C) $\left[M T^{-1} C^{-1}\right]$
(D) $\left[M T^{-2} C^{-1}\right]$

Akshaya Rs
Akshaya Rs
Numerade Educator
01:44

Problem 109

The respective number of significant figure for the numbers $23.023,0.0003$ and $2.1 \times 10^{-3}$ are
(A) $4,4,2$
(B) $5,1,2$
(C) $5,1,5$
(D) $5,5,2$

Akshaya Rs
Akshaya Rs
Numerade Educator
01:24

Problem 110

Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it. If the percentage errors in the measurement of the current and the voltage difference are $3 \%$ each, then error in the value of resistance of the wire is
(A) $6 \%$
(B) Zero
(C) $1 \%$
(D) $3 \%$

Akshaya Rs
Akshaya Rs
Numerade Educator
01:51

Problem 111

Let $\left[\epsilon_{0}\right]$ denote the dimensional formula of the permittivity of vacuum. If $M=$ mass, $L=$ length, $T=$ time and $A=$ electric current, then
(A) $\left[\epsilon_{0}\right]=\left[M^{-1} L^{-3} T^{4} A^{2}\right]$
(B) $\left[\epsilon_{0}\right]=\left[M^{-1} L^{2} T^{-1} A^{-2}\right]$
(C) $\left[\in_{0}\right]=\left[\begin{array}{ll} \left.M^{-1} L^{2} T^{-1} A\right]\end{array}\right.$
(D) $\left[\epsilon_{0}\right]=\left[M^{-1} L^{-3} T^{2} A\right]$

Akshaya Rs
Akshaya Rs
Numerade Educator
01:38

Problem 112

The current voltage relation of diode is given by $I=(\mathrm{e} 1000 \mathrm{~V} / \mathrm{T}-1) \mathrm{mA}$, where the applied voltage $\mathrm{V}$
is in volts and the temperature $\mathrm{T}$ is in degree Kelvin. If a student makes an error measuring $\pm 0.01 V$ while measuring the current of $5 \mathrm{~mA}$ at $300 \mathrm{~K}$, what will be the error in the value of current in $\mathrm{mA}$ ?
(A) $0.2 \mathrm{~mA}$
(B) $0.252 \mathrm{~mA}$
(C) $0.5 \mathrm{~mA}$
(D) $0.05 \mathrm{~mA}$

Akshaya Rs
Akshaya Rs
Numerade Educator
01:45

Problem 113

The period of oscillation of a simple pendulum is $T=2 \pi \sqrt{\frac{L}{g}} .$ Measured value of $L$ is $20.0 \mathrm{~cm}$ known to 1 mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using a wrist watch of 1s resolution. The accuracy in the determination of $g$ is
(A) $3 \%$
(B) $1 \%$
(C) $5 \%$
(D) $2 \%$

Akshaya Rs
Akshaya Rs
Numerade Educator
02:02

Problem 114

A student measures the time period of 100 oscillations of a simple pendulum four times. The data set is $90 \mathrm{~s}, 91 \mathrm{~s}, 95 \mathrm{~s}$, and $92 \mathrm{~s}$. If the minimum division in the measuring clock is $1 \mathrm{~s}$, then the reported mean time should be:
(A) $92 \pm 5.0 \mathrm{~s}$
(B) $92 \pm 1.8 \mathrm{~s}$
(C) $92 \pm 3 \mathrm{~s}$
(D) $92 \pm 2 \mathrm{~s}$

Akshaya Rs
Akshaya Rs
Numerade Educator
02:19

Problem 115

A screw gauge with a pitch of $0.5 \mathrm{~mm}$ and a circular scale with 50 divisions is used to measure the thick= ness of a thin sheet of Aluminium. Before starting the measurement, it is found that when the two jaws of the screw gauge are brought in contact, the $45^{\text {th }}$ division coincides with the main scale line and that the zero of the main scale is barely visible. What is the thickness of the sheet if the main scale reading is $0.5 \mathrm{~mm}$ and the $25^{\text {th }}$ division coincides with the main scale line?
(A) $0.80 \mathrm{~mm}$
(B) $0.70 \mathrm{~mm}$
(C) $0.50 \mathrm{~mm}$
(D) $0.75 \mathrm{~mm}$

Akshaya Rs
Akshaya Rs
Numerade Educator