Coefficients of Friction

Q. Two bodies of masses $m_1$ and $m_2$ are placed on a horizontal table with coefficient of friction $\mu$ and are joined by a spring. Initially, the spring has its natural length. If $F$ is minimum force which, when continuously applied on $m_1$, will make the other block $m_2$ just move ($k$ is the spring constant) and $x$ is elongation in spring at that instant

1. $x=\frac{\mu m_{2}g}{k}$
2. $x=\frac{2\mu m_{2}g}{k}$
3. $F=\mu m_{2}g+\frac{\mu m_{1}g}{2}$
4. $F=\mu m_{1}g+\frac{\mu m_{2}g}{2}$

Q. A circular road of radius 1000 m has banking angle ${45}^{\circ }$. The maximum safe speed of a car having mass 2000 kg will be, if the coefficient of friction between tyre and road is 0.5

1. 99 m/s
2. 172 m/s
3. 124 m/s
4. 86 m/s

Q. The coefficient of friction can never be more than 1.

1. False
2. True

Q. For any given pair of surfaces, the coefficient of friction is maximum in case of limiting friction.

1. False
2. True

Q. The coefficient of friction has no unit.

1. False
2. True

Q. A plank with a box on it at one end is gradually raised about the other end. As the angle of inclination with the horizontal reaches ${30}^0$, the box starts to slip and slides $4m$ down the plank in $4s$. The coefficients of static and kinetic friction between the box and the plank will be, respectively

1. $0.4$ and $0.3$
2. $0.6$ and $0.6$
3. $0.6$ and $0.5$
4. $0.5$ and $0.6$

Q.

A block pressed against the vertical wall is in equilibrium. The minimum coefficient of friction is

1. $0.4$
2. $0.2$
3. $0.5$
4. None of these

Q. For a body on a horizontal surface, coefficients of static and kinetic frictions are $0.4$ and $0.2$, respectively. When the body is in uniform motion on the surface, a horizontal force equal in magnitude to limiting friction is applied on it. The acceleration produced is

1. $0.4\text{g}$
2. $0.1\text{g}$
3. $0.2\text{g}$
4. $0.6\text{g}$

Q. A block begins to slide down a rough inclined plane of angle ${45}^{\circ }$ and moves $1m$ in $\sqrt[4]{42}s$. What is the coefficient of friction $\mu$, between the plane and the block?
(Take $g=10m/s^2)$

1. $0.6$
2. $0.8$
3. $0.5$
4. $0.4$

Q. A box of mass $\text{8 kg}$ is placed on a rough inclined plane of angle $\theta$ with horizontal. Its downward motion can be prevented by applying an upward pull $F$ and it can be made to slide upwards by applying a force $2F$. The coefficient of friction between the box and the inclined plane is

1. $\frac{\tan \theta }{3}$
2. $3\tan \theta$
3. $\frac{\tan \theta }{2}$
4. $2\tan \theta$