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Guide to Physics IIT JEE

Ravi Raj Dudeja

Chapter 7

Conservation of Momentum - all with Video Answers

Educators

Chapter Questions

01:00

Problem 1

A rocket having fuel as its bulk is initially at rest. Neglecting the effect of gravity, when fuel is burning at a constant rate, acceleration $a$ of the rocket with respect to time $t$ is best represented by one of the graphs given below.

Dominador Tan
Dominador Tan
Numerade Educator
03:17

Problem 1

A particle at rest suddenly disintegrates into two particles of equal masses which start moving. The two fragments will
(a) move opposite with unequal speeds.
(b) move in any direction with any speed.
(c) move in same direction with equal speeds.
(d) move opposite with equal speed.

Suman Saurav Thakur
Suman Saurav Thakur
Numerade Educator
10:38

Problem 2

Two girls of equal mass $m$ jump off from the border line of a stationery carriage of mass $M$ with same horizontal velocity $u$ relative to the carriage. Neglecting the effect of friction

(a) they will impart greater velocity to the carriage by jumping of simultaneously.
(b) they will impart greater velocity to the carriage by jumping one after the other.
(c) they will impart greater velocity to the carriage in whatever manner they jump off.
(d) insufficient data to reply.

Naresh Bagrecha
Naresh Bagrecha
Numerade Educator
01:41

Problem 2

A bomb of mass $9 \mathrm{~kg}$ explodes into two pieces of mass $3 \mathrm{~kg}$ and $6 \mathrm{~kg}$. The velocity of mass $3 \mathrm{~kg}$ is $16 \mathrm{~ms}^{-1}$. The kinetic ennergy of mass $6 \mathrm{~kg}$ in joule is
(a) 768
(b) 96
(c) 384
(d) 192

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:16

Problem 3

In the shown system friction is meaningless. The carriage of mass $M$ has constant initial velocity $u$ along a straight horizontal track when at $t=0$, it starts raining. The rain drops have a vertical velocity $u^{\prime}$ and result into addition of mass $m$ per second to the carriage. The velocity of carraige after $T$ second of start of rain is
(a) $\frac{M u}{M+m t}$
(b) $\frac{M u+m u^{\prime}}{M+m t}$
(c) $\frac{\left(u+u^{\prime}\right)(M+m)}{M}$
(d) $\frac{M\left(u+u^{\prime}\right)}{m t}$

Narayan Hari
Narayan Hari
Numerade Educator
01:42

Problem 4

A massive ball moving with a speed $v$ collides with a tiny ball having a very small mass then immediately after the impact, the second ball will move with a speed approximately equal to
(a) $\infty$
(b) $v / 2$
(c) $v$
(d) $2 v$

Saman Zulfiqar
Saman Zulfiqar
Numerade Educator
02:41

Problem 4

A system consists of mass $M$ and $m$. The centre of mass of the system is
(a) nearer to $m$.
(b) at the position of large mass.
(c) nearer to $M$.
(d) in the middle.

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
03:49

Problem 4

A man weighing $80 \mathrm{~kg}$ is standing on a trolley weighing $320 \mathrm{~kg}$. The trolly is resting on frictionless horizontal rails. If the man starts walking on the trolley along the rails at a speed $1 \mathrm{~ms}^{-1}$ then after 4 second his displacement relative to the ground will be
(a) $3.0 \mathrm{~m}$
(b) $3.2 \mathrm{~m}$
(c) $4.8 \mathrm{~m}$
(d) $5 \mathrm{~m}$

Nishant Kumar
Nishant Kumar
Numerade Educator
01:37

Problem 4

A boy of mass $m \mathrm{~kg}$ boards a trolley of mass $2 m$ moving with constant speed $u$ along a horizontal track. Neglecting friction, if the boy jumps vertically up with reference to the trolley to catch hold of a branch of a tree, the speed of trolley after the boy has jumped off is
(a) $u$
(b) $2 u$
(c) $\frac{u}{2}$
(d) $\frac{3 u}{4}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
03:01

Problem 5

Two similar bogies $A$ and $B$ of same mass $M$ (empty bogie) move with constant velocities $v_A$ and $v_B$ towards each other on smooth parallel tracks. At an instant a boy of mass $m$ from bogie $A$ and a boy of same mass from bogie $B$ exchange their positioin by jumping in a direction normal to the track, then bogie $A$ stops while $B$ keeps moving in the same direction with new velocity $v_g$. The initial velocities of bogie $A$ and $B$ are given by
(a) $\frac{M-m}{m} v_B, \frac{M-m}{M} v_B$
(b) $\frac{m v_B}{(M-m)}, \frac{M v_B}{(M-m)}$
(c) $\frac{m v_B}{(M+m)}, \frac{M v_B}{(M+m)}$
(d) $\frac{(M-m) v_B}{m}, \frac{(M-m) v_B}{M}$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:49

Problem 6

A bomb of mass $m$ is moving in $x$ direction with velocity $u$ when it separates into masses $\frac{1}{3} m$ and $\frac{2}{3} m$ moving horizontally in the same plane. If an additional energy of $4 \mathrm{mu} u^2$ is generated, the relative speed of two masses is
(a) $3 u$
(b) $4 u$
(c) $6 u$
(d) $8 u$.

Saman Zulfiqar
Saman Zulfiqar
Numerade Educator
02:53

Problem 6

A neutron, with kinetic energy $K E$ and moving with velocity $v$, collides head on with a nucleus of mass number A perfectly elastically. The fraction of total energy possessed by the neutron transferred to nucleus is
(a) $\frac{4 A}{(A-1)^2}$
(b) $\left(\frac{A-1}{A+1}\right)^2$
(c) $\left(\frac{A+1}{2 A}\right)^2$
(d) $\left(\frac{A-1}{2 A}\right)^2$

Saman Zulfiqar
Saman Zulfiqar
Numerade Educator
10:38

Problem 7

A ray of energy $14.2 \mathrm{MeV}$ is emitted from a ${ }^{60} \mathrm{Co}$ nucleus. The recoil energy of the Co nucleus is nearly
(a) $3 \times 10^{-16} \mathrm{~J}$
(b) $3 \times 10^{-15} \mathrm{~J}$
(c) $3 \times 10^{-14} \mathrm{~J}$
(d) $3 \times 10^{-13} \mathrm{~J}$

Hafiz Shahzaib
Hafiz Shahzaib
Numerade Educator
02:44

Problem 7

A rope ladder of length $L$ is attached to a balloon of mass $M$. As the man of mass $m$ climbs the ladder into the balloon basket the balloon comes downs by a vertical distance $s$. Then, increase in potential energy of man divided by increase in potential energy of balloon is
(a) $\frac{L-s}{s}$
(b) $\frac{L}{s}$
(c) $\frac{s}{L-s}$
(d) $L-s$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
02:19

Problem 8

$\mathrm{A} 0.5 \mathrm{~kg}$ block slides from $A$ on horizontal track with an initial speed of $3 \mathrm{~ms}^{-1}$ towards a weightless horizontal spring of length $1 \mathrm{~m}$ and force constant $2 \mathrm{Nm}^{-1}$. The part $A B$ of the track is frictionless and the part $\mathrm{BC}$ has the coefficient of static and kinetic friction as 0.22 and 0.20 respectively. If the distance $A B$ and $B D$ are $2 \mathrm{~m}$ and $2.14 \mathrm{~m}$ respectively, the total distance through which the block moves before it comes to rest completely is
(a) $2.5 \mathrm{~m}$
(b) $4.42 \mathrm{~m}$
(c) $4.24 \mathrm{~m}$
(d) $2.44 \mathrm{~m}$.
(Based on IIT 1983)

Yuva S
Yuva S
Numerade Educator
00:47

Problem 9

A shell is fired from a cannon with a velocity $V^{\prime}(\mathrm{m} / \mathrm{s})$ at an angle $\theta$ with the horizontal direction. At the highest point in its path it explodes into two pieces of equal mass. One of the pieces retraces its path to the cannon and the speed (in $\mathrm{m} / \mathrm{s}$ ) of the other piece immediately after the explosion is
(a) $3 \mathrm{~V} \cos \theta$
(b) $2 \mathrm{~V} \cos \theta$
(c) $\frac{3}{2} \mathrm{~V} \cos \theta$
(d) $\frac{\sqrt{3}}{2} \mathrm{~V} \cos \theta$

Hast Aggarwal
Hast Aggarwal
Numerade Educator
03:55

Problem 10

Two particles of masses $m_1$ and $m_2$ in projectile motion have velocities $\vec{v}_1$ and $\vec{v}_2$ respectively at time $t=0$. They strike at time $t_0$ and their velocities become $v_1^{\prime}$ and $v_2^{\prime}$ at time $2 t_0$ while still moving in air. The value of $\left|\left(m_1 \overrightarrow{v_1^{\prime}}+m_2 \overrightarrow{v_2^{\prime}}\right)-\left(m_1 \overrightarrow{v_1}+m_2 \overrightarrow{v_2}\right)\right|$ is
(a) zero
(b) $\left(m_1+m_2\right) g t_0$
(c) $2\left(m_1+m_2\right) g t_0$
(d) $\frac{1}{2}\left(m_1+m_2\right) g t_0$

RZ
Rubeena Zulfiqar
Numerade Educator
03:12

Problem 11

A light and a heavy body have equal kinetic energy. Which one has a greater momentum?
(a) The heavy body
(b) The light body
(c) Both
(d) Cannot be said

Suman Saurav Thakur
Suman Saurav Thakur
Numerade Educator
02:35

Problem 12

The linear momentum of a body is increased by $50 \%$. Its kinetic energy will increase by
(a) $150 \%$
(b) $125 \%$
(c) $100 \%$
(d) $50 \%$

Suman Saurav Thakur
Suman Saurav Thakur
Numerade Educator
01:56

Problem 13

Two unequal masses are tied together with a compressed spring. When the cord is burnt with a match stick releasing the spring; the two masses fly apart with equal
(a) momentum
(b) acceleration
(c) kinetic energy
(d) speed

Suman Saurav Thakur
Suman Saurav Thakur
Numerade Educator
01:18

Problem 15

Two masses of $1 \mathrm{~g}$ and $4 \mathrm{~g}$ are moving with kinetic energy in the ratio $4: 1$. What is the ratio of their linear mementum?
(a) $6: 1$
(b) $4: 1$
(c) $1: 2$
(d) $1: 1$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
02:03

Problem 16

On a stationary sail boat air is blown from a fan attached to the boat. The boat
(a) moves in opposite direction in which air is blows.
(b) does not move.
(c) move in same direction in which air blows.
(d) spins around.

Joseph Fritchman
Joseph Fritchman
Numerade Educator
01:48

Problem 17

The spacecraft of mass $M$ moving with a velocity $v$ in free space explodes and breaks up into two pieces. If after explosion a piece of mass $m$ comes to rest, the other piece of spacecraft will have a velocity
(a) $\frac{M v}{(M-m)}$
(b) $\frac{M v}{(M+m)}$
(c) $m V /(M-m)$
(d) $\frac{m v}{(M+m)}$

Suman Saurav Thakur
Suman Saurav Thakur
Numerade Educator
01:29

Problem 18

A shell explodes and many pieces fly off in different directions. The following is conserved
(a) kinetic energy
(b) momentum
(c) both
(d) none

Ajay Singhal
Ajay Singhal
Numerade Educator
03:12

Problem 19

A light and a heavy body have equal momenta. Which one has greater kinetic enerty?
(a) The heavy body
(b) The light body
(c) Both
(d) None

Suman Saurav Thakur
Suman Saurav Thakur
Numerade Educator
01:24

Problem 20

A bird on the floor of an air tight box which is being carried by a boy starts flying. The boy feels that the box is now
(a) lighter
(b) heavier
(c) shows no change in weight
(d) lighter in the beginning and then heavier

Sachin Rao
Sachin Rao
Numerade Educator
01:19

Problem 21

Two bodies of mass $m_A$ and $m_B$ have equal kinetic energy. The ratio of their momenta is
(a) $\sqrt{m_A}: \sqrt{m_B}$
(b) $m_A^2: m_g^2$
(c) $m_A: m_B$
(d) $m_B: m_A$

Narendra Kumar
Narendra Kumar
Numerade Educator
02:03

Problem 22

A bullet weighing $50 \mathrm{gm}$ leaves the gun with a velocity of $30 \mathrm{~ms}^{-1}$. If the recoil speed imparted to the gun is $1 \mathrm{~ms}^{-1}$, the mass of the gun
(a) $1.5 \mathrm{~kg}$
(b) $15 \mathrm{~kg}$
(c) $20 \mathrm{~kg}$
(d) $30 \mathrm{~kg}$

Narendra Kumar
Narendra Kumar
Numerade Educator
02:12

Problem 23

If the kinetic energy of a body becomes four times of its initial value, then the new momentum will be
(a) double
(b) 3 times
(c) 4 times
(d) unchanged

Suman Saurav Thakur
Suman Saurav Thakur
Numerade Educator
01:41

Problem 24

A particle of mass $m$ is moving in a horizontal circle of radius $r$ with uniform speed $v$. When it moves from one point to a diametrically opposite point its
(a) $K E$ changes by $m v^2$.
(b) $K E$ changes by $(1 / 4) m v^2$.
(c) momentum does not change.
(d) momentum changes by $2 \mathrm{mv}$.

RZ
Rubeena Zulfiqar
Numerade Educator
01:12

Problem 25

Kinetic energy of a body of mass $m$ and momentum $p$ is given by
(a) $p^2 m$
(b) $m^2 / 2 p$
(c) $m p$
(d) $p^2 / 2 m$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
02:08

Problem 26

When the velocity of a body is doubled
(a) kinetic energy is doubled.
(b) acceleration is doubled.
(c) momentum is doubled.
(d) potential energy is doubled.

Vysakh M
Vysakh M
Numerade Educator
01:25

Problem 27

A surface is hit elastically and normally by $n$ balls per unit time. All the balls have the same mass $m$ and move with the same velocity $u$. The force on the surface is
(a) $1 / 2 m n u^2$
(b) $m n u^2$
(c) $2 m n u^2$
(d) $2 m n u$

Saman Zulfiqar
Saman Zulfiqar
Numerade Educator
02:49

Problem 29

A body of mass $m$ at rest explodes into three pieces, two of which of mass $m / 4$ each are thrown off in perpendicular directions with velocity of $3 \mathrm{~ms}^{-1}$ and $4 \mathrm{~ms}^{-1}$ respectively. The third piece will be thrown off with a velocity of
(a) $3 \mathrm{~ms}^{-1}$
(b) $2.5 \mathrm{~ms}^{-1}$
(c) $2 \mathrm{~ms}^{-1}$
(d) $1.5 \mathrm{~ms}^{-1}$

Saman Zulfiqar
Saman Zulfiqar
Numerade Educator
03:04

Problem 30

A body of mass $1 \mathrm{~kg}$ initially at rest explodes and breaks into three fregments of masses in the ratio $1: 1: 3$. The two pieces of equal mass fly off perpendicular to each other with a speed of $15 \mathrm{~ms}^{-1}$ each. The speed of the heavier fregment is
(a) $45 \mathrm{~ms}^{-1}$
(b) $15 \mathrm{~ms}^{-1}$
(c) $5 \mathrm{~ms}^{-1}$
(d) $5 \sqrt{2} \mathrm{~ms}^{-1}$

Suman Saurav Thakur
Suman Saurav Thakur
Numerade Educator
02:40

Problem 31

A block of mass $2 \mathrm{~m}$ moving with constant velocity $3 \vec{v}$ collides with another block of mass $m$ which is at rest and stick to it. The velocity of the compound block after the collision is
(a) $\vec{v}$
(b) $3 \vec{v} / 2$
(c) $2 \vec{v}$
(d) $3 \vec{v}$

RZ
Rubeena Zulfiqar
Numerade Educator
02:27

Problem 32

When two bodies collide elestically then the quantity conserved is
(a) kinetic energy
(b) mometum
(c) both
(d) none

RZ
Rubeena Zulfiqar
Numerade Educator
00:49

Problem 33

Two balls at the same temprature collide. What is conserved?
(a) Momentum
(b) Kinetic energy
(c) Velocity
(d) Temperature

Narendra Kumar
Narendra Kumar
Numerade Educator
01:49

Problem 34

Two balls each of mass $0.25 \mathrm{~kg}$ are moving towards each other in a straight line, one at $3 \mathrm{~ms}^{-1}$ and the other at $1 \mathrm{~ms}^{-1}$ collide. The balls stick together after the collision. The magnitude of the final velocity of the combined mass is
(a) $1 / 2 \mathrm{~ms}^{-1}$
(b) $1 \mathrm{~ms}^{-1}$
(c) $2 \mathrm{~ms}^{-1}$
(d) $4 \mathrm{~ms}^{-1}$

RZ
Rubeena Zulfiqar
Numerade Educator
04:22

Problem 35

A bullet weighing $10 \mathrm{~g}$ and moving at $300 \mathrm{~ms}^{-1}$ strikes a $5 \mathrm{~kg}$ block of ice and drops dead. The ice block is sitting on frictionless level surface. The speed of the block, after the collision is
(a) $60 \mathrm{~ms}^{-1}$
(b) $160 \mathrm{~ms}^{-1}$
(c) $16 \mathrm{~ms}^{-1}$
(d) $6 \mathrm{~ms}^{-1}$

Saman Zulfiqar
Saman Zulfiqar
Numerade Educator
02:59

Problem 36

A body of mass $m$ moving with a constant velocity $v$ hits another body of the same mass moving with same velocity $\mathrm{v}$ but in the opposite direction, and sticks to it. The velocity of the compound body after collision is
(a) zero
(b) $v$
(c) $2 v$
(d) $v / 2$

Paul Gabriel
Paul Gabriel
Numerade Educator
02:17

Problem 37

A bullet of mass ' $a$ ' and velocity ' $b$ ' is fired into a large block of wood of mass ' $c$ '. The final velocity of the system is
(a) $\frac{a b}{a+c}$
(b) $\frac{b}{a}(\mathrm{a}+\mathrm{c})$
(c) $\frac{c b}{(a+b)}$
(d) $\frac{b}{c}(\mathrm{a}+\mathrm{b})$

Mkhitar Hobosyan
Mkhitar Hobosyan
Numerade Educator
01:18

Problem 38

A mass $m_1$ moves with a great velocity. If it strikes another mass $m_2$ at rest in a head on collision it comes back along its path with a low speed after collision. Then
(a) $m_1>m_2$
(b) $m_1=m_2$
(c) $m_1<m_2$
(d) there is relation between $m_1$ and $m_2$

Saman Zulfiqar
Saman Zulfiqar
Numerade Educator
02:04

Problem 39

39. Two solid rubber balls $A$ and $B$ having masses $200 \mathrm{~g}$ and $400 \mathrm{~g}$ respectively are moving in opposite directions with velocity of $A$ equal to $0.3 \mathrm{~ms}^{-1}$. After collision the two balls come to rest then the velocity of $B$ is
(a) $-0.15 \mathrm{~ms}^{-1}$
(b) $0.15 \mathrm{~ms}^{-1}$
(c) $1.5 \mathrm{~ms}^{-1}$
(d) none of these

Narendra Kumar
Narendra Kumar
Numerade Educator
02:40

Problem 40

A body of mass m moving with a constant velocity $v$ hits another body of the same mass at rest and sticks to it. The velocity to the compound body after collision is
(a) zero
(b) $v / 2$
(c) $v$
(d) $2 v$

RZ
Rubeena Zulfiqar
Numerade Educator
01:49

Problem 41

A body of mass $2 \mathrm{~kg}$ moving with a velocity of 3 $\mathrm{ms}^{-1}$ collides head on with a body of mass $1 \mathrm{~kg}$ moving with a velocity of $4 \mathrm{~ms}^{-1}$ in opposite direction. After collision the two bodies stick together and move with a common velocity
(a) $\frac{2}{3} \mathrm{~ms}^{-1}$
(b) $\frac{3}{4} \mathrm{~ms}^{-1}$
(c) $\frac{1}{4} \mathrm{~ms}^{-1}$
(d) $\frac{1}{3} \mathrm{~ms}^{-1}$

RZ
Rubeena Zulfiqar
Numerade Educator
05:23

Problem 42

A steel ball moving with a velocity $\vec{v}$ collides with an identical ball originally at rest. The velocity of the first ball after the collision is
(a) $\left(-\frac{1}{2}\right) \vec{v}$
(b) $-\vec{v}$
(c) $\vec{v}$
(d) zero

Paul Gabriel
Paul Gabriel
Numerade Educator
02:42

Problem 43

Two perfectly elastic particles $A$ and $B$ of equal masses travelling along the line joining them with velocity 15 $\mathrm{ms}^{-1}$ and $10 \mathrm{~ms}^{-1}$ respectively collide. Their velocities after the elastic collision will be (in $\mathrm{ms}^{-1}$ ) respectively
(a) 20 and 5
(b) 10 and 15
(c) 5 and 20
(d) 0 and 25

RZ
Rubeena Zulfiqar
Numerade Educator
02:53

Problem 44

A neutron travelling with a velocity $v$ and kinetic energy $K E$ collides elastically head on with the nucleus of an atom of mass number $A$ at rest. The fraction of total energy retained by the neutron is
(a) $\left(\frac{A}{A+1}\right)$
(b) $\left(\frac{A}{A+1}\right)^2$
(c) $\left(\frac{A-1}{A+1}\right)$
(d) $\left(\frac{A-1}{A+1}\right)^2$

Saman Zulfiqar
Saman Zulfiqar
Numerade Educator
02:34

Problem 46

A sphere of mass $m$ moving with a constant velocity $v$ hits another stationary sphere of the same mass. If $e$ is the coefficient of restitution, then the ratio of the velocities of the two spheres after collision will be

(a) $\left(\frac{e+1}{e-1}\right)$
(b) $\left(\frac{e-1}{e+1}\right)$
(c) $\left(\frac{1-e}{e+1}\right)$
(d) $\left(\frac{1+e}{e-1}\right)$

RZ
Rubeena Zulfiqar
Numerade Educator
03:11

Problem 49

Two skaters $A$ and $B$ of mass $50 \mathrm{~kg}$ and $70 \mathrm{~kg}$ respectively stand facing each other $6 \mathrm{~m}$ apart. They then pull on a rope stretched between them. How far has each moved when they meet?
(a) $A$ moves $3.5 \mathrm{~m}$ and $B 2.5 \mathrm{~m}$
(b) $A$ moves $2 \mathrm{~m}$ and $B 4 \mathrm{~m}$
(c) both have moved $3 \mathrm{~m}$
(d) both have moved $2.5 \mathrm{~m}$

Rashmi Sinha
Rashmi Sinha
Numerade Educator
03:41

Problem 50

Two carts on horizontal straight rails are pushed apart by an explosion of a powder charge $Q$ placed between the carts. Suppose the coefficient of friction of the two are equal and $200 \mathrm{~kg}$ cart travels a distance of $36 \mathrm{~m}$ and stops. The distance covered by the cart weighing 300 $\mathrm{kg}$ is
(a) $12 \mathrm{~m}$
(b) $16 \mathrm{~m}$
(c) $24 \mathrm{~m}$
(d) $32 \mathrm{~m}$

Saman Zulfiqar
Saman Zulfiqar
Numerade Educator
02:46

Problem 51

Two particles of mass $m$ and $2 m$ are at a distance $d$ apart. Under their mutual gravitational force they start moving towards each other. The acceleration of their centre of mass when they are $d / 2$ apart is
(a) $89 \mathrm{~m} / \mathrm{d}^2$
(b) $44 \mathrm{~m} / \mathrm{d}^2$
(c) $29 \mathrm{~m} / \mathrm{d}^2$
(d) zero

Saman Zulfiqar
Saman Zulfiqar
Numerade Educator
04:33

Problem 52

In case of explosion of a bomb which of the following does not change?
(a) Chemical energy
(b) Energy
(c) Kinetic energy
(d) Mechanical energy

Suman Saurav Thakur
Suman Saurav Thakur
Numerade Educator
02:31

Problem 53

Which of the following is nonconservative force?
(a) Electric force
(b) Elastic force
(c) Viscous force
(d) Gravitational force

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:17

Problem 54

A ball of mass $m$ moving with velocity $v$ collides elastically with wall and rebounds. The change in momentum of the ball will be
(a) $4 m v$
(b) $2 m v$
(c) $m v$
(d) zero

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:45

Problem 55

A nucleus of mass number $A$ originally at rest emits $\alpha$ particle with speed $v$. What will be the recoil speed of the daughter nucleus?

(a) $\frac{v}{A-4}$
(b) $\frac{v}{A+4}$
(c) $\frac{4 v}{A-4}$
(d) $\frac{4 v}{A+4}$

Mirza Aslam Beig
Mirza Aslam Beig
Numerade Educator
03:37

Problem 56

A ball is dropped from a height $h$. It rebounds from the ground a number of times. Given that the coefficient of restitution is $e$, to what height does it go after $n^{\text {th }}$ rebounding?
(a) $h / e^n$
(b) $h / e^{2 n}$
(c) $h e^n$
(d) $h e^{2 n}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:33

Problem 57

A moving mass of $8 \mathrm{~kg}$ collides elastically with a stationary mass of $2 \mathrm{~kg}$. If $\mathrm{KE}$ be the initial kinetic energy of the moving mass, the kinetic energy left with it after the collision will be
(a) $0.08 \mathrm{KE}$
(b) $0.36 \mathrm{KE}$
(c) $0.64 \mathrm{KE}$
(d) $0.80 \mathrm{KE}$

Vysakh M
Vysakh M
Numerade Educator
02:33

Problem 58

In the elastic collision of heavy vehicle moving with a velocity $10 \mathrm{~ms}^{-1}$ and a small stone at rest, the stone will fly away with a velocity equal to
(a) $40 \mathrm{~ms}^{-1}$
(b) $20 \mathrm{~ms}^{-1}$
(c) $10 \mathrm{~ms}^{-1}$
(d) $5 \mathrm{~ms}^{-1}$

Saman Zulfiqar
Saman Zulfiqar
Numerade Educator
03:11

Problem 59

A ball strikes against the floor and returns with double the velocity. In which type of collision is it possible?
(a) Inelastic
(b) Perfectly inelastic
(c) Perfectly elastic
(d) Not possible

Kristela Garcia
Kristela Garcia
Numerade Educator
01:49

Problem 60

A ball kept in a closed container moves in it making collision with the walls. The container is kept on a smooth surface. The velocity of the centre of mass of
(a) the ball remains fixed.
(b) the ball relative to container remains fixed.
(c) the container remains fixed.
(d) both container and ball remain fixed.

Dharmendra Jain
Dharmendra Jain
Numerade Educator
02:58

Problem 61

A ball $A$ of mass $m$ is moving with a velocity $v$ along north. It collides with another ball $B$ of same mass moving with velocity $v$ along east. After the collision both balls stick together and move along northeast. The velocity of the combination is
(a) $v / \sqrt{2}$
(b) $v$
(c) $\sqrt{2} v$
(d) $2 v$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:29

Problem 62

A ball moving with velocity of $9 \mathrm{~ms}^{-1}$ collides with another similar stationary ball. After the collision both the balls move in directions making an angle of $30^{\circ}$ with the initial direction. After the collision their speed will be
(a) $0.52 \mathrm{~ms}^{-1}$
(b) $2.6 \mathrm{~ms}^{-1}$
(c) $5.2 \mathrm{~ms}^{-1}$
(d) $52 \mathrm{~ms}^{-1}$

Vysakh M
Vysakh M
Numerade Educator
00:56

Problem 63

The physical quantiy which is conserved for all types of collision is
(a) $K E$
(b) $M$
(c) $\vec{p}$
(d) $L$

Suman Saurav Thakur
Suman Saurav Thakur
Numerade Educator
01:44

Problem 64

Three particles $\alpha, \beta$ and $\gamma$ of equal mass are moving with the same velocity $v$ along the medians of an equilateral triangle. These particles collide at the centreoid $G$ of a triangle. After collision $\alpha$ becomes stationary, $\beta$ retraces its path with velocity $v$ then the magnitude and direction of $\gamma$ will be
(a) $v$ and in the direction of $\beta$
(b) $v$ and in the direction of $\gamma$
(c) $v$ and opposite to $\beta$
(d) $v$ and in the direction of $\alpha$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
03:20

Problem 65

Two particles each of mass $m$ and travelling with velocities $u_1$ and $u_2$ collide perfectly inelastically. The loss of energy will be
(a) $\frac{1}{4} m\left(u_1-u_2\right)^2$
(b) $\frac{1}{2} m\left(u_1-u_2\right)^2$
(c) $2 m\left(u_1-u_2\right)^2$
(d) $m\left(\mathrm{u}_1-u_2\right)^2$

RZ
Rubeena Zulfiqar
Numerade Educator
02:40

Problem 66

A particle of mass $m_1$ and moving with velocity $v_1$ collides head on with another stationary particle of mass $m_2$ elastically. If after the collision their velocities are $v_1$ and $v_2$ then under the condition $m_1=$ $m_2$ their values will be
(a) $v_1=0, v_2=0$
(b) $v_1=u_1, v_2=u_2$
(c) $v_1=0, v_2=u_1$
(d) $v_2=0, v_1=u_1$

Saman Zulfiqar
Saman Zulfiqar
Numerade Educator
01:42

Problem 68

Two similar balls $P$ and $Q$ having velocities of 0.5 $\mathrm{ms}^{-1}$ and $-0.3 \mathrm{~ms}^{-1}$ respectively collide elastically. The velocities of $P$ and $Q$ after the collision will respectively be
(a) $0.3 \mathrm{~ms}^{-1}$ and $0.5 \mathrm{~ms}^{-1}$
(b) $-0.5 \mathrm{~ms}^{-1}$ and $0.3 \mathrm{~ms}^{-1}$
(c) $0.5 \mathrm{~ms}^{-1}$ and $0.3 \mathrm{~ms}^{-1}$
(d) $-0.3 \mathrm{~ms}^{-1}$ and $0.5 \mathrm{~ms}^{-1}$

Saman Zulfiqar
Saman Zulfiqar
Numerade Educator
02:26

Problem 69

A ball falls from a height of $5 \mathrm{~m}$ and strikes the roof of a lift. If at the time of collision, lift is moving in the upward direction with a velocity of $1 \mathrm{~ms}^{-1}$. Then the velocity with which the ball rebounds after collision will be
(a) $13 \mathrm{~ms}^{-1}$ upwards
(b) $12 \mathrm{~ms}^{-1}$ downwards
(c) $12 \mathrm{~ms}^{-1}$ upwards
(d) $11 \mathrm{~ms}^{-1}$ downwards

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
02:01

Problem 70

A particle of mass $m$ strikes a wall with a velocity $v$ making an angle $\theta$ with the wall and rebounds. The change in momentum of the particle will be
(a) $-2 m_{\vec{v}} \cos \theta$
(b) 0
(c) $2 m_{\vec{v}}$
(d) $2 m \vec{v} \sin \theta$

Narendra Kumar
Narendra Kumar
Numerade Educator
01:28

Problem 72

Two masses $m_1$ and $m_2$ are connected to a spring of spring constant $k$ at two ends. The spring is compressed by $y$ and released. The distance moved by $m_1$ before it comes to a stop for the first time is
(a) $\frac{m_1 y}{m_1+m 2}$
(b) $\frac{m_2 y}{m_1+m 2}$
(c) $\frac{2 m_1 y}{m_1+m 2}$
(d) $\frac{2 m_2 y}{m_1+m 2}$

Ajay Singhal
Ajay Singhal
Numerade Educator
03:52

Problem 73

A radioactive nucleus decays by $\beta$ emission. Both $\beta$ and neutrino move mutually at right angels with momentum $6 \times 10^{-21} \mathrm{~kg} \mathrm{~ms}^{-1}$ and $3 \times 10^{-21} \mathrm{~kg} \mathrm{~ms}^{-1}$. The direction of recoil of nucleus with respect to electron is
(a) $\tan ^{-1}\left(\frac{1}{2}\right)$
(b) $\tan ^{-1}(2)$
(c) $180-\tan ^{-1}\left(\frac{1}{2}\right)$
(d) $180-\tan ^{-1}(2)$

Joseph Petrullo
Joseph Petrullo
Numerade Educator