# Tag: physics

### Questions Related to physics

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

1. $1$

2. $15$

3. $\cfrac { 1 }{ \sqrt { 3 } }$

4. $\cfrac { \sqrt { 3 } }{ 2 }$

Correct Option: C
Explanation:

$\mu =tan\theta \ =tan30=\frac { 1 }{ \sqrt { 3 } } \$

The coefficient of friction between a chain & a table is m. If a chain is placed on a horizontal table so that a part of it is hanging from one end, the minimum fraction of length of the chain that can be on the table, so that the chain may not slip off is

1. $\frac{\mu}{\mu + 1}$

2. $\frac{1}{\mu + 1}$

3. 1

4. Zero

Correct Option: A

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?

1. $26.7^o$.

2. $16.7^o$.

3. $36.7^o$.

4. $46.7^o$.

Correct Option: B

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

1. $\dfrac{1}{3}tan\theta$

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

3. $\dfrac{2}{3}tan\theta$

4. $\dfrac{2}{3}sin\theta$

Correct Option: A

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:

1. $\frac { 1 }{ 2 } tan\alpha$

2. $2sin\alpha$

3. $cot\alpha$

4. $2tan\alpha$

Correct Option: A

A block is kept on a horizontal table. The table is undergoing simple harmonic motion of frequency $3\, Hz$ in a horizontal plane. The coefficient of static friction between the block and the table surface is $0.72$. Find the maximum amplitude of the table at which the block does not slip on the surface $(g = 10\, ms^{-2})$

1. $0.01m$

2. $0.02m$

3. $0.03m$

4. $0.04m$

Correct Option: B

A lineman of mass 60 kg is holding a vertical pole. The coefficient of static friction between his hands and the pole is 0.5.If the able to climb up the pole,Then the minimum force with which he should press the pole with his hands $[g = 10 ms^{-2}] is$

1. 1200 N

2. 600 N

3. 300 N

4. 150 N

Correct Option: C

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

1. $\mu^2h$

2. $\mu/h$

3. $\mu h$

4. $\mu^2h^2$

Correct Option: C

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

1. $9.8\ N$

2. $0.7\times 9.8\times \sqrt { 3 } N$

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

4. $0.7\times 9.8\ N$

Correct Option: A
Explanation:

The force applied on the body that is on the inclined plane is given as,

$F = mg\sin \theta$

$F = 2 \times 9.8 \times \sin 30^\circ$

$= 9.8\;{\rm{N}}$

The limiting friction force between the block and the inclined plane is given as,

$f = \mu mg\cos \theta$

$f = 0.7 \times 2 \times 9.8\cos 30^\circ$

$= 11.88\;{\rm{N}}$

Since the limiting friction force is greater than the force that tends to slide the body.

Thus, the body will be at rest and the force of friction on the block is $9.8\;{\rm{N}}$.

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:

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

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

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

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

Correct Option: A
Explanation:

$\dfrac { { V } _{ a } }{ n } =\sqrt { 2Lg\left( \sin\theta -\mu \cos\theta \right) } \quad \longrightarrow \left( 1 \right)$

${ V } _{ a }=\sqrt { 2Lg\sin\theta } \quad \longrightarrow \left( 2 \right)$
By putting equ(2) in eq(1) we get
$\dfrac { \sqrt { 2Lg\sin\theta } }{ n } =\sqrt { 2Lg\left( \sin\theta -\mu \cos\theta \right) }$
$\dfrac { 2Lg\sin\theta }{ { n }^{ 2 } } =2Lg\left( \sin\theta -\mu \cos\theta \right)$
$\dfrac { \sin\theta }{ { n }^{ 2 } } =\sin\theta -\mu \cos\theta$
$\mu \cos\theta =\sin\theta -\dfrac { \sin\theta }{ { n }^{ 2 } }$
$\mu \cos\theta =\sin\theta \left( 1-\dfrac { 1 }{ { n }^{ 2 } } \right)$
$\mu =\tan\theta \left( 1-\dfrac { 1 }{ { n }^{ 2 } } \right)$