Motion along a rough inclined plane - class-XI

Question 1 Multiple Choice (Single Answer)

A block released from rest from the top of a smooth inclined plane of angle $\theta _1$ reaches the bottom in time $t _1$. The same block released from rest from the top of another smooth inclined plane of angle $\theta _2$, reaches the bottom in time $t _2$. If the two inclined planes have the same height, the relation between $t _1$ and $t _2$ is

$\cfrac{t _2}{t _1} = \left(\cfrac{sin \theta _1}{sin \theta _2}\right)^{1/2}$
$\cfrac{t _2}{t _1} = 1$
$\cfrac{t _2}{t _1} = \left(\cfrac{sin \theta _1}{sin \theta _2}\right)$
$\cfrac{t _2}{t _1} = \left(\cfrac{sin^2 \theta _1}{sin^2 \theta _2}\right)$

Question 2 Multiple Choice (Single Answer)

The coefficient of friction between two surfaces is 0.2. The angle of friction is

sin$^{-1}$(0.2)
cos $^{-1}$(0.2)
tan$^{-1}$(0.1)
cot$^{-1}$(5)

Question 3 Multiple Choice (Single Answer)

If angle of repose is ${30}^{o}$, then coefficient of friction will be

$1$
$15$
$\cfrac { 1 }{ \sqrt { 3 } } $
$\cfrac { \sqrt { 3 } }{ 2 } $

Question 4 Multiple Choice (Single Answer)

A piece of wood of mass $150$ g rests on an inclined plane. The co-efficient of friction between the surfaces in contact is $0.3$. To what maximum extent the plane may be inclined without allowing the piece to clip down?

$26.7^o$.
$16.7^o$.
$36.7^o$.
$46.7^o$.

Question 5 Multiple Choice (Single Answer)

A solid cylinder is placed on a rough inclined surface of inclination $\theta$. Minimum value of coefficient of static friction between the cylinder and the surface so that the cylinder rolls without slipping is

$\dfrac{1}{3}tan\theta$
$\dfrac{1}{3}sin\theta$
$\dfrac{2}{3}tan\theta$
$\dfrac{2}{3}sin\theta$

Question 6 Multiple Choice (Single Answer)

The upper half of an inclined plane with inclination $\alpha $ is perfectly smooth while the lower half is rough, a body starts from rest at the top of the inclined and comes to rest again at the bottom of it. The coefficient of friction for the lower half of the incline is:

$\frac { 1 }{ 2 } tan\alpha $
$2sin\alpha $
$cot\alpha $
$2tan\alpha $

Question 7 Multiple Choice (Single Answer)

A light ladder is supported on a rough floor and lens against a smooth wall, touching the wall at height 'h' above the floor. A man climbs up the ladder until the base of the ladder is on the verge of slipping. The coefficient of statice friction between the foot of the ladder and the floort is $\mu$. The horizontal distance moved by the man is

$\mu^2h$
$\mu/h$
$\mu h$
$\mu^2h^2$

Question 8 Multiple Choice (Single Answer)

A block of mass $2\ kg$ rests on a rough inclined plane making an angle of ${30}^{o}$ with the horizontal. The coefficient of static friction between the block and the plane is $0.7$. The frictional force on the block is

$9.8\ N$
$0.7\times 9.8\times \sqrt { 3 } N$
$9.8\times \sqrt { 3 } N$
$0.7\times 9.8\ N$

Question 9 Multiple Choice (Single Answer)

An object is placed on the surface of a smooth inclined plane of inclination $\theta$. It takes time $t$ to reach the bottom. If the same object is allowed to slide down a rough inclined plane of same inclination $\theta $, it takes times nth to reach the bottom where $n$ number greater than $1$. The coefficient of friction $\mu$ is given by:

$\mu =\tan { \theta \left( 1-1/{ n }^{ 2 } \right) } $
$\mu =\cot { \theta \left( 1-1/{ n }^{ 2 } \right) } $
${ \mu =\tan { \theta \left( 1-1/{ n }^{ 2 } \right) } }^{ 1/2 }$
${ \mu =\cot { \theta \left( 1-1/{ n }^{ 2 } \right) } }^{ 1/2 }$

Question 10 Multiple Choice (Single Answer)

A body of weight 20 N is on a horizontal surface, minimum force applied to pull it when applied force makes an angle $60^0$ with horizontal (angle of friction a = $30^0$) is:

20 N
20 $\sqrt{3}$ N
$\dfrac{20}{\sqrt{3}}$ N
zero

Motion along a rough inclined plane - class-XI

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