Finding Friction's Magnitude

Q.

A block of mass m is lying a horizontal surface of coefficient of friction $\mu$. A force F is applied to the block at an angle $\theta$ with the horizontal. The block will move with a minimum force F if

1. $\mu =tan\theta$

2. $\mu =cot\theta$

3. $\mu =sin\theta$

4. $\mu =cos\theta$

Q.

Figure shows a man standing stationary with respect to a horizontal conveyor belt. If the coefficient of static friction between the man's shoes and the belt is 0.2, up to what acceleration of the belt can the man continue to be stationary relative to the belt? (Mass of the man = 65 kg).

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Q.

A block released from rest from the top of a smooth inclined plane of inclination ${45}^{\circ }$ takes $t$ seconds to reach the bottom. The same block released from rest from the top of a rough inclined plane of the same inclination of ${45}^{\circ }$ takes $2t$ seconds to reach the bottom. The coefficient of friction is

1. $\sqrt{0.75}$

2. $\sqrt{0.5}$

3. $0.5$

4. $0.75$

Q.

A block of weight 200 N is pulled along a rough horizontal surface at a constant speed by a force of 100 N acting at an angle of ${30}^{\circ }$ above the horizontal. The coefficient of friction between the block and the surface is

1. 0.58

2. 0.43

3. 0.75

4. 0.85

Q.

A body is moving down a long inclined plane of angle of inclination $\theta$. The coefficient of friction between the body and the plane varies as $\mu =0.5x$, where $x$is the distance moved down the plane. The body will have the maximum velocity when it has travelled a distance x given by

1. $x=2tan\theta$

2. $x=\frac{2}{tan\theta }$

3. $x=\sqrt{2}cot\theta$

4. $x=\frac{\sqrt{2}}{cot\theta }$

Q.

A block of mass 5 kg is lying on a rough horizontal surface. The coefficients of static and kinetic friction between the block and the surface respectively are 0.7 and 0.5. A horizontal force just sufficient to move the block is applied to it. If the force continues to act even after the block has started moving, what will be the acceleration of the block? Take $g=10m{s}^{-2}$.

1. $1m{s}^{-2}$

2. $2m{s}^{-2}$

3. $3m{s}^{-2}$

4. $4m{s}^{-2}$

Q.

An insect crawls up a hemispherical surface very slowly (see the figure). The coefficient of friction between the surface and the insect is $\frac{1}{3}$. If the 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

1. $cot\alpha =3$

2. $tan\alpha =3$

3. $sec\alpha =3$

4. $cosec\alpha =3$

Q.

What is the maximum value of the force F such that the block shown in the arrangement, does not move?

1. 10 N

2. 15 N

3. 12 N

4. 20 N

Q.

An object is gently placed on a long conveyer belt moving with a uniform speed of $5m{s}^{-1}$. If the coefficient of friction between the block and the belt is 0.5, how far will the box move on the belt (relative to belt) before coming to rest? Take $g=10m{s}^{-2}$.

1. 2.0 m

2. 2.5 m

3. 3.0 m

4. 3.5 m

Q.

A boy of mass 40 kg is climbing a vertical pole at a constant speed. If the coefficient of friction between his palms and the pole is 0.8 and $g=10m{s}^{-2}$, the horizontal force that he is applying on the pole is

1. 300 N

2. 400 N

3. 500 N

4. 600 N