Genius Physics (Class 11) - For IIT-JEE and CBSE

Pradeep Kshetrapal

Chapter 5

Friction - all with Video Answers

Educators

Chapter Questions

Problem 1

If a ladder weighing $250 \mathrm{~N}$ is placed against a smooth vertical wall having coefficient of friction between it and floor is $0.3$, then what is the maximum force of friction available at the point of contact between the ladder and the floor
(a) $75 \mathrm{~N}$
(b) $50 \mathrm{~N}$
(c) $35 \mathrm{~N}$
(d) $25 \mathrm{~N}$

Charles Machakwa

Charles Machakwa

Numerade Educator

Problem 2

On the horizontal surface of a truck ( $\mu=0.6$ ), a block of mass $1 \mathrm{~kg}$ is placed. If the truck is accelerating at the rate of $5 \mathrm{~m} / \mathrm{sec}^{2}$ then frictional force on the block will be
(a) $5 N$
(b) $6 \mathrm{~N}$
(c) $5.88 \mathrm{~N}$
(d) $8 N$

Charles Machakwa

Charles Machakwa

Numerade Educator

Problem 3

A block of mass $2 \mathrm{~kg}$ is kept on the floor. The coefficient of static friction is $0.4$. If a force $F$ of $2.5 \mathrm{~N}$ is applied on the block as shown in the figure, the frictional force between the block and the floor will be [MP PET
(a) $2.5 \mathrm{~N}$
(b) $5 \mathrm{~N}$
(c) $7.84 N$
(d) $10 \mathrm{~N}$

Charles Machakwa

Charles Machakwa

Numerade Educator

Problem 4

A block $A$ with mass $100 \mathrm{~kg}$ is resting on another block $B$ of mass $200 \mathrm{~kg}$. As shown in figure a horizontal rope tied to a wall holds it. The coefficient of friction between $A$ and $B$ is $0.2$ while coefficient of friction between $B$ and the ground is o.3. The minimum required force $F$ to start moving $B$ will be
(a) $900 \mathrm{~N}$
(b) $100 \mathrm{~N}$
(c) $1100 N$
(d) $1200 \mathrm{~N}$

Charles Machakwa

Charles Machakwa

Numerade Educator

Problem 5

A $20 \mathrm{~kg}$ block is initially at rest on a rough horizontal surface. A horizontal force of $75 \mathrm{~N}$ is required to set the block in motion. After it is in motion, a horizontal force of $60 N$ is required to keep the block moving with constant speed. The coefficient of static friction is
(a) $0.38$
(b) $0.44$
(c) $0.52$
(d) $0.60$

Charles Machakwa

Charles Machakwa

Numerade Educator

Problem 6

A block of mass $M$ is placed on a rough floor of a lift. The coefficient of friction between the block and the floor is $\mu$. When the lift falls freely, the block is pulled horizontally on the floor. What will be the force of friction
(a) $\mu \mathrm{Mg}$
(b) $\mu \mathrm{Mg} / 2$
(c) $2 \mu \mathrm{Mg}$
(d) None of these

Charles Machakwa

Charles Machakwa

Numerade Educator

Problem 7

A body of $5 \mathrm{~kg}$ weight kept on a rough inclined plane of angle $30^{\circ}$ starts sliding with a constant velocity. Then the coefficient of friction is (assume $g=10 \mathrm{~m} / \mathrm{s}^{2}$ )
(a) $1 / \sqrt{3}$
(b) $2 / \sqrt{3}$
(c) $\sqrt{3}$
(d) $2 \sqrt{3}$

Charles Machakwa

Charles Machakwa

Numerade Educator

Problem 8

The upper half of an inclined plane of inclination $\theta$ is perfectly smooth while the lower half is rough. A body starting from the rest at top comes back to rest at the bottom if the coefficient of friction for the lower half is given
(a) $\mu=\sin \theta$
(b) $\mu=\cot \theta$
(c) $\mu=2 \cos \theta$
(d) $\mu=2 \tan \theta$

Charles Machakwa

Charles Machakwa

Numerade Educator

Problem 9

What is the maximum value of the force $F$ such that the block shown in the arrangement, does not move $(\mu=1 / 2 \sqrt{3})$
[IIT-JEE (Sereening) 2003]
(a) $20 \mathrm{~N}$
(b) $10 \mathrm{~N}$
(c) $12 N$
(d) $15 N$

Charles Machakwa

Charles Machakwa

Numerade Educator

Problem 10

A block of mass $m$ rests on a rough horizontal surface as shown in the figure. Coefficient of friction between the block and the surface is $\mu$. A force $F=m g$ acting at angle $\theta$ with the vertical side of the block pulls it. In which of the following cases the block can be pulled along the surface
(a) $\tan \theta \geq \mu$
(b) $\cot \theta \geq \mu$
(c) $\tan \theta / 2 \geq \mu$
(d) $\cot \theta / 2 \geq \mu$

Dheeraj Sharma

Numerade Educator

Problem 11

A body of mass $10 \mathrm{~kg}$ is lying on a rough plane inclined at an angle of $30^{\circ}$ to the horizontal and the coefficient of friction is o.5. The minimum force required to pull the body up the plane is
(a) $914 N$
(b) $91.4 N$
(c) $9.14 \mathrm{~N}$
(d) $0.914 N$

Charles Machakwa

Charles Machakwa

Numerade Educator

Problem 12

A block of mass $10 \mathrm{~kg}$ is placed on a rough horizontal surface having coefficient of friction $\mu=0.5$. If a horizontal force of $100 N$ is acting on it, then acceleration of the block will be
(a) $0.5 \mathrm{~m} / \mathrm{s}^{2}$
(b) $5 \mathrm{~m} / \mathrm{s}^{2}$
(c) $10 \mathrm{~m} / \mathrm{s}^{2}$
(d) $15 \mathrm{~m} / \mathrm{s}^{2}$

Charles Machakwa

Charles Machakwa

Numerade Educator

Problem 13

A body of weight $64 N$ is pushed with just enough force to start it moving across a horizontal floor and the same force continues to act afterwards. If the coefficients of static and dynamic friction are $0.6$ and $0.4$ respectively, the acceleration of the body will be (Acceleration due to gravity $=g$ )
(a) $\frac{g}{6.4}$
(b) $0.64 g$
(c) $\frac{g}{32}$
(d) $0.2 g$

Charles Machakwa

Charles Machakwa

Numerade Educator

Problem 14

If a block moving up at $\theta=30^{\circ}$ with a velocity $5 \mathrm{~m} / \mathrm{s}$, stops after $0.5 \mathrm{sec}$, then what is $\mu$
(a) $0.5$
(b) $1.25$
(c) $0.6$
(d) None of these

Charles Machakwa

Charles Machakwa

Numerade Educator

Problem 15

A body of mass $5 \mathrm{~kg}$ rests on a rough horizontal surface of coefficient of friction o.2. The body is pulled through a distance of $10 m$ by a horizontal force of $25 N$. The kinetic energy acquired by it is $\left(g=10 \mathrm{~ms}^{2}\right)$ [BAMCET (Med.) 2000]
(a) $330 \mathrm{~J}$
(b) $150^{\circ} J$
(c) $100 J$
(d) $50 \mathrm{~J}$

Charles Machakwa

Charles Machakwa

Numerade Educator

Problem 16

300 Joule of work is done in sliding a $2 \mathrm{~kg}$. block up an inclined plane to a height of 10 meters. Taking value of acceleration due to gravity $^{4} g$ ' to be $10 \mathrm{~m} / \mathrm{s}^{2}$, work done against friction is $\quad$ [MP PMT 2002]
(a) $100 . J$
(b) $200 \mathrm{~J}$
(c) $300 J$
(d) Zero

Charles Machakwa

Charles Machakwa

Numerade Educator

Problem 17

A block of mass $1 \mathrm{~kg}$ slides down on a rough inclined plane of inclination $60^{\circ}$ starting from its top. If the coefficient of kinetic friction is $0.5$ and length of the plane is $1 m$, then work done against friction is (Take $g=9.8 \mathrm{~m} / \mathrm{s}^{2}$ ) $\quad$ [AFMC 2000; KCET (Engg./Med.) 2001]
(a) $9.82 J$
(b) $4.94 \mathrm{~J}$
(c) $2.45 J$
(d) $1.96 J$

Charles Machakwa

Charles Machakwa

Numerade Educator

Problem 18

A block of mass $50 \mathrm{~kg}$ slides over a horizontal distance of $1 \mathrm{~m}$. If the coefficient of friction between their surfaces is o.2, then work done against friction is [CBSE PMT 1999, 2000; AIIMS 2000; BHU 2001]
(a) $98 J$
(b) $72 . J$
(c) $56 J$
(d) $34 J$

Charles Machakwa

Charles Machakwa

Numerade Educator

Problem 19

A $4 k g$ block $A$ is placed on the top of a $8 k g$ block $B$ which rests on a smooth table. $A$ just slips on $B$ when a force of $12 \mathrm{~N}$ is applied on $A$. Then the maximum horizontal force on $\mathrm{B}$ to make both $A$ and $B$ move together, is
(a) $12 \mathrm{~N}$
(b) $24 N$
(c) $36 \mathrm{~N}$
(d) $48 \mathrm{~N}$

Saikat Chatterjee

Saikat Chatterjee

Numerade Educator

Problem 20

A body $A$ of mass $1 \mathrm{~kg}$ rests on a smooth surface. Another body $B$ of mass $0.2 \mathrm{~kg}$ is placed over $A$ as shown. The coefficient of static friction between $A$ and $B$ is $0.15-B$ will begin to slide on $A$ if $A$ is pulled with a force greater than
(a) $1.764 N$
(b) $0.1764 N$
(c) $0.3 N$
(d) It will not slide for any $F$

Charles Machakwa

Charles Machakwa

Numerade Educator

Problem 21

A block $A$ of mass $2 \mathrm{~kg}$ rests on another block $B$ of mass $8 \mathrm{~kg}$ which rests on a horizontal floor. The coefficient of friction between $A$ and $B$ is $0.2$, while that between $B$ and floor is $0.5$. When a horizontal force of $25 \mathrm{~N}$ is applied on the block $B$, the force of friction between $A$ and $B$ is
(a) Zero
(b) $3.9 \mathrm{~N}$
(c) $5.0 \mathrm{~N}$
(d) $49 \mathrm{~N}$

Charles Machakwa

Charles Machakwa

Numerade Educator

Problem 22

An insect crawls up a hemispherical surface very slowly (see the figure). The coefficient of friction between the insect and the surface is $1 / 3$. If the line joining the centre of the hemispherical surface to the insect makes an angle $\alpha$ with the vertical, the maximum possible value of $\alpha$ is given by [IIT-JEE (Screening) 2001]
(a) $\cot \alpha=3$
(b) $\tan \alpha=3$
(c) $\sec \alpha=3$
(d) $\operatorname{cosec} \alpha=3$

Charles Machakwa

Charles Machakwa

Numerade Educator

Problem 23

Two blocks of mass $M_{1}$ and $M_{2}$ are connected with a string passing over a pulley as shown in the figure. The block $M_{1}$ lies on a horizontal surface. The coefficient of friction between the block $M_{1}$ and horizontal surface is $\mu$. The system accelerates. What additional mass $m$ should be placed on the block $M_{1}$ so that the system does not accelerate
(a) $\frac{M_{2}-M_{1}}{\mu}$
(b) $\frac{M_{2}}{\mu}-M_{1}$
(c) $M_{2}-\frac{M_{1}}{\mu}$
(d) $\left(M_{2}-M_{1}\right) \mu$

Charles Machakwa

Charles Machakwa

Numerade Educator

Problem 24

The coefficient of kinetic friction is $0.03$ in the diagram where mass $m_{2}=20 \mathrm{~kg}$ and $m_{1}=4 \mathrm{~kg}$. The acceleration of the block shall be $\left(g=10 \mathrm{~ms}^{-2}\right)$
(a) $1.8 \mathrm{~ms}^{-2}$
(b) $0.8 \mathrm{~ms}^{-2}$
(c) $1.4 \mathrm{~ms}^{-2}$
(d) $0.4 \mathrm{~ms}^{-2}$

Charles Machakwa

Charles Machakwa

Numerade Educator

Problem 25

A heavy uniform chain lies on a horizontal table top. If the coefficient of friction between the chain and the table surface is $0.25$, then the maximum fraction of the length of the chain that can hang over one edge of the table is
(a) $20 \%$
(b) $25 \%$
(c) $35 \%$
(d) $15 \%$

Narayan Hari

Numerade Educator

Problem 26

A body takes just twice the time as long to slide down a plane inclined at $30^{\circ}$ to the horizontal as if the plane were frictionless. The coefficient of friction between the body and the plane is [JIPMER 1999]
(a) $\frac{\sqrt{3}}{4}$
(b) $\sqrt{3}$
(c) $\frac{4}{3}$
(d) $\frac{3}{4}$

Charles Machakwa

Charles Machakwa

Numerade Educator

Problem 27

A marble block of mass $2 \mathrm{~kg}$ lying on ice when given a velocity of $6 \mathrm{~m} / \mathrm{s}$ is stopped by friction in $10 \mathrm{~s}$. Then the coefficient of friction is
(a) $0.01$
(b) $0.02$
(c) $0.03$
(d) $0.06$

Charles Machakwa

Charles Machakwa

Numerade Educator

Problem 28

A $2 \mathrm{~kg}$ mass starts from rest on an inclined smooth surface with inclination $30^{\circ}$ and length $2 \mathrm{~m}$. How much will it travel before coming to rest on a surface with coefficient of friction $0.25$
(a) $4 m$
(b) $6 \mathrm{~m}$
(c) $8 \mathrm{~m}$
(d) $2 \mathrm{~m}$

Charles Machakwa

Charles Machakwa

Numerade Educator

Problem 29

A motorcycle is travelling on a curved track of radius $500 m$ if the coefficient of friction between road and tyres is $0.5 .$ The speed avoiding skidding will be [MH CET (Med.) 2001]
(a) $50 \mathrm{~m} / \mathrm{s}$
(b) $75 \mathrm{~m} / \mathrm{s}$
(c) $25 \mathrm{~m} / \mathrm{s}$
(d) $35 \mathrm{~m} / \mathrm{s}$

Charles Machakwa

Charles Machakwa

Numerade Educator

Problem 30

A horizontal force of $10 \mathrm{~N}$ is necessary to just hold a block stationary against a wall. The coefficient of friction between the block and the wall is $0.2$. The weight of the block is [AIFEE 2003]
(a) $2 \underline{N}$
(b) $20 \mathrm{~N}$
(c) $50 \mathrm{~N}$
(d) $100 \mathrm{~N}$

Charles Machakwa

Charles Machakwa

Numerade Educator

Problem 31

A body of mass $2 k g$ is kept by pressing to a vertical wall by a force of $100 \mathrm{~N}$. The friction between wall and body is o.3. Then the frictional force is equal to [Orissa JEE 20o3]
(a) $6 \mathrm{~N}$
(b) $20 \mathrm{~N}$
(c) $600 \mathrm{~N}$
(d) $700 \mathrm{~N}$

Charles Machakwa

Charles Machakwa

Numerade Educator

Problem 32

A fireman of mass $60 \mathrm{~kg}$ slides down a pole. He is pressing the pole with a force of $600 \mathrm{~N}$. The coefficient of friction between the hands and the pole is o.5, with what acceleration will the fireman slide down $\left(g=10 \mathrm{~m} / \mathrm{s}^{2}\right) \quad$ [Pb. PMT 2002]
(a) $1 \mathrm{~m} / \mathrm{s}^{2}$
(b) $2.5 \mathrm{~m} / \mathrm{s}^{2}$
(c) $10 \mathrm{~m} / \mathrm{s}^{2}$
(d) $5 \mathrm{~m} / \mathrm{s}^{2}$

Charles Machakwa

Charles Machakwa

Numerade Educator

Problem 33

The system shown in the figure is in equilibrium. The maximum value of $W$, so that the maximum value of static frictional force on $100 \mathrm{~kg}$. body is $450 \mathrm{~N}$, will be
(a) $100 \mathrm{~N}$
(b) $250 \mathrm{~N}$
(c) $450 \mathrm{~N}$
(d) $1000 \mathrm{~N}$

Charles Machakwa

Charles Machakwa

Numerade Educator