Finding Friction's Magnitude

Q.

On a rough horizontal surface, a body of mass 2 kg is given a velocity of 10 m/s. If the coefficient of friction is 0.2 and g=10 $m/s^2$, the body will stop after covering a distance of

1. 250 m

2. 50 m

3. 10 m

4. 25 m

Q.

A 2 kg block is placed over a 4 kg block and both are placed on a smooth horizontal surface. The coefficient of friction between the blocks is 0.20. Find the acceleration of the two blocks if a horizontal force of 12 N is applied to the upper block. Take g = 10 $m/s^2$.

1. a = 4 m/s, a = 4 m/s

2. a = 1 m/s, a = 4 m/s

3. None of these

4. a =2 m/s, a =2 m/s

Q.

Find the minimum force 'F' and the angle '$\alpha$' at which it should be applied to a block of mass 'm' kept on a horizontal surface such that the block starts moving. Given that the coefficient of friction between the block and surface is $\mu$.

1. $F_{min}=\frac{\mu mg}{\sqrt{1+{\mu }^2}},\alpha =ta{n}^{-1}\frac{1}{\mu }$

2. $F_{min}=\frac{\mu mg}{\sqrt{1+{\mu }^2}},\alpha =ta{n}^{-1}\frac{1}{\mu }$

3. None of these

4. $F_{min}=\frac{\mu mg}{\sqrt{1+{\mu }^2}},\alpha =ta{n}^{-1}\mu$

Q. Harry carried out an experiment to find out how different surfaces (A, B, C and D) affect the distance of a car travelling at 50 km/h needed to stop once the brakes applied. The results are shown below in given table. Which type of road will provide the most friction for the car to stop?

हैरी यह ज्ञात करने के लिए एक प्रयोग करता है, कि भिन्न-भिन्न पृष्ठ (A, B, C तथा D) 50 km/h से गतिशील एक कार को ब्रेक लगाकर रोकने के लिए आवश्यक दूरी को किस प्रकार प्रभावित करते हैं। परिणाम नीचे दी गई सारणी में दर्शाए गए हैं तथा किस प्रकार की सड़क कार के रूकने के लिए सर्वाधिक घर्षण प्रदान करेगी?

Types of road surface (सड़क के पृष्ठ के प्रकार)	Stopping distance (m) (रूकने की दूरी (m))
A	18
B	25
C	19
D	17

1. A
2. B
3. C
4. D

Q.

A block of mass 'm' is supported on a rough wall by applying a force P as shown in figure. Coefficient of static friction between block and wall is ${\mu }_s$

For what range of values of P, the block remains in static equilibrium?

1. None of these

2. 

3. 

4. 

Q. A block is gently placed on a conveyor belt moving horizontally at a constant speed. After $t=4\text{s}$, the velocity of the block becomes equal to the velocity of the belt. If the coefficient of static friction between the block and the belt is $\mu =0.2$, then what is the velocity of the conveyor belt ?

1. $2\text{m/s}$
2. $4\text{m/s}$
3. $6\text{m/s}$
4. $8\text{m/s}$

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. $\sqrt{0.5}$

2. $\sqrt{0.75}$

3. $0.5$

4. $0.75$

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. Figure shows a pair of pin jointed gripper tongs holding an object weighing $2000\text{N}$. The coefficient of friction $\mu$ at the gripping surface is $0.1$. $X-X^{\prime }$ is the line of action of the input force and $Y-Y^{\prime }$ is the line of application of normal gripping force. If the pin-joint is assumed as frictionless, the magnitude of force $F$ required to hold the weight (in $\text{N}$) is

Q.

Q. A block of mass $15\text{kg}$ is acted upon by a force $25\text{N}$ at an angle ${37}^{\circ }$ with the horizontal in a direction as shown in figure. The coefficient of static friction($\mu$) between the block and horizontal surface is $0.2$ . Find the frictional force acting on the block, so that it doesn't move. Take $(g=10{\text{m/s}}^2)$.

1. $33\text{N}$
2. $13\text{N}$
3. $10\text{N}$
4. $20\text{N}$

Q. A block of mass $m$ is lying on a horizontal surface and the coefficient of static friction between the block and surface is $\mu$. Force $F$ is applied at an angle $\theta$ with the horizontal in two different ways as shown in the figure.


For just moving the block along horizontal direction, identify the correct statement.

1. If $\mu =0$ , $F$ is lesser in case $\left(a\right)$
2. If $\mu =0$ , $F$ is lesser in case $\left(b\right)$
3. If $\mu \ne 0$, $F$ is lesser in case $\left(a\right)$
4. If $\mu \ne 0$, $F$ is lesser in case $\left(b\right)$

Q. The friction force acting on the bike is

1. $\frac{2m{v}^{2}tan\theta }{\ell \sqrt{4+ta{n}^2\theta }}$
2. $\frac{2m{v}^{2}ta{n}^2\theta }{\ell \sqrt{2+ta{n}^2\theta }}$
3. $\frac{m{v}^{2}ta{n}^2\theta }{\ell \sqrt{4+ta{n}^2\theta }}$
4. $\frac{m{v}^{2}ta{n}^2\theta }{\ell \sqrt{2+ta{n}^2\theta }}$

Q. A car moving at a speed of $36km/hr$ is taking a turn on a circular road of radius $50m$. A small wooden plate is kept on the seat with its plane perpendicular to the radius of the circular road (Figure). A small block of mass $100g$ is kept on the seat which rests against the plate. The friction coefficient between the block and the plate is $\mu =0.58$ (a) Find the normal contact force exerted by the plate on the block (b) The plate is slowly turned so that the angle between the normal to the plate and the radius of the road slowly increases. Find the angle at which the block will just start sliding on the plane

Q. A force $F=(\hat{i}+4\hat{j})\text{N}$ acts on the block shown. The force of friction acting on the block is :

1. $-\hat{i}\text{N}$
2. $-18\hat{i}\text{N}$
3. $-2.4\hat{i}\text{N}$
4. $-3\hat{i}\text{N}$

Q. A circular racket of radius 300 m is backed at an angle of ${15}^0$. The coefficient of friction between the wheels of a race car and the road is 0.2. The optimum speed of the car to avoid wear and tear on its tyres is then
( Take tan ${15}^0=0.27,g=10m{s}^{-2}$)

1. $10\sqrt{3}m{s}^{-1}$
2. $9\sqrt{10}m{s}^{-1}$
3. $\sqrt{10}m{s}^{-1}$
4. $2\sqrt{10}m{s}^{-1}$

Q. A block of mass $3\text{kg}$ is at rest on a rough inclined plane as shown in the figure. The magnitude of net force exerted by the surface on the block will be $(g=10{\text{m/s}}^2)$

1. $26\text{N}$
2. $19.5\text{N}$
3. $10\text{N}$
4. $30\text{N}$