Maximum Push Using Friction

Q.

Three identical rigid circular cylinders A, B and C are arranged on smooth inclined surfaces as shown in figure. The least value of $\theta$ that prevent the arrangement from collapse is?

1. $ta{n}^{-1}\left(\frac{1}{4\sqrt{3}}\right)$

2. $ta{n}^{-1}\left(\frac{1}{2\sqrt{3}}\right)$

3. $ta{n}^{-1}\left(\frac{1}{3\sqrt{3}}\right)$

4. $ta{n}^{-1}\left(\frac{1}{4\sqrt{3}}\right)$

Q. What is meant by banking of road? What is need of banking of roads? Obtain an expression for the maximum speed with which a vehicle can safely negotiate a curved road banked at an angle $\theta$. The coefficient of friction between the wheels is and the road is $\mu$.

Q.

The brakes of an unloaded lorry of mass 1000 kg will slow it down from 40 to 20 km/h in 7.5 s. How long will they take to stop it from a speed of 30 km/h, if it has taken on a load of
2200 kg?

Q. If ${\mu }_s$ and ${\mu }_k$ represent the coefficient of static and kinetic friction respectively with appropriate suffixes for the two bodies shown, find the acceleration of the system $[$ Take $g=10{\text{m/s}}^2]$

1. $10{\text{m/s}}^2$
2. $20{\text{m/s}}^2$
3. $15.5{\text{m/s}}^2$
4. Zero

Q. The coefficient of static and kinetic friction between a body of mass $m=1$ unit and the surface are $.75$ and $.50$ respectively. A force is applied to the body to maintain constant acceleration when the body is in motion. This constant force is:

1. $g/4$
2. $g/2$
3. $3g/4$
4. $g$

Q. Find the minimum value of $F$ for which the system is in equilibrium? $[$ Take $g={\text{10 m/s}}^2]$

1. $30\text{N}$
2. $10\text{N}$
3. $15\text{N}$
4. $20\text{N}$

Q. A rope of mass $m$ is attached to a block of mass $M$ lying on a horizontal surface. The block is pulled along the surface by applying a force $F$ on the free end of the rope. If $\mu$ is the coefficient of friction between block and the surface, the force exerted by the rope on the block is

1. $\frac{m}{(M+m)}(F-\mu mg)$
2. $\frac{M}{(M+m)}(F-\mu Mg)$
3. $\frac{m}{M}(F+\mu mg)$
4. $\frac{M}{(m+M)}(F+\mu Mg)$

Q. If ${\mu }_s$ and ${\mu }_k$ represent the coefficient of static and kinetic friction respectively with appropriate suffixes for the two bodies shown, find the acceleration of the system $[$ Take $g=10{\text{m/s}}^2]$

1. $10{\text{m/s}}^2$
2. $20{\text{m/s}}^2$
3. $15.5{\text{m/s}}^2$
4. Zero

Q. The coefficient of friction between the tyres and road is $0.4$. The minimum distance covered before attaining a speed of $8{\text{ms}}^{-1}$ starting from rest is nearly $(g=10m/s^2)$

1. 8.0 m
2. 4.0 m
3. 10.0 m
4. 16.0 m

Q. The pulley is given an acceleration $a_0=2{\text{m/s}}^2$ starting from rest. A cable is connected to a block $A$ of mass $50\text{kg}$ as shown. Neglect the mass of the pulley. If $\mu =0.3$ between the block and the floor, then the tension in the cable is:

1. $200\text{N}$
2. $250\text{N}$
3. $300\text{N}$
4. $350\text{N}$

Q. A block of mass $1kg$ starts moving at $t=0$ with speed $2m/s$ on rough horizontal surface with coefficient of friction $0.2$. A horizontal force $F$ is applied in the same direction of velocity which varies with time shown in figure (b). Find the speed of particle at $t=3s$ ($g=10m/s^2)$

1. $1m/s$
2. zero
3. $5m/s$
4. $2m/s$

Q. If the coefficient of friction between $A$ and $B$ is $\mu$, the maximum acceleration of the wedge $A$ for which $B$ remains at rest with respect to the wedge is

1. $\mu g$
2. $g\left(\frac{1+\mu }{1-\mu }\right)$
3. $g\left(\frac{1-\mu }{1+\mu }\right)$
4. $\frac{g}{\mu }$

Q. The force $F_1$ that is necessary to move a body up an inclined plane is double the force $F_2$ that is necessary to just prevent it from sliding down, then: ( Given that $\varphi$ is angle of repose, $\theta$ is angle of inclined plane and $\text{w}$ is weight of the body)

1. $F_2=\text{w sin}(\theta -\varphi )\text{sec}\varphi$
2. $F_1=\text{w sin}(\theta -\varphi )\text{sec}\varphi$
3. $\text{tan}\varphi =3\text{tan}\theta$
4. $\text{tan}\theta =3\text{tan}\varphi$

Q. Two block $A$ and $B$ of equal mass $3\text{kg}$ each are connected over a massless pulley as shown in figure. The block $A$ is placed on a rough inclined plane of angle ${30}^{\circ }$. The coefficient of friction between block $A$ and inclined plane is $0.6$. The friction force acting on the block $A$ is
(Assume $g=10{\text{ms}}^{-2}$ )

1. Zero
2. $15.6\text{N}$
3. $18\text{N}$
4. $15\text{N}$

Q. A block of mass 5 kg is kept over a rough horizontal surface. A time varying force acts on it along the horizontal given by F = 2t. The block starts slipping at t = 2.5 s and its acceleration at t = 3 s is $0.4{\text{m/s}}^2$. The summation of coefficients of static and kinetic friction is (take $g=10{\text{ms}}^{-2}$)

Q. An insect crawls up a hemispherical surface very slowly (figure). The coefficient of friction between the insect and the surface is $\frac{1}{3}$. If the line joining the centre of hemispherical surface to the insect makes an angle $\alpha$ with the vertical, the maximum possible value of $\alpha$ is given by

1. $\cot \alpha =3$
2. $\tan \alpha =3$
3. $\sec \alpha =3$
4. $\text{cosec}\alpha =3$

Q. A block of mass $m$ is placed on a prism of mass $M$. The inclined surface is smooth and inclination with horizontal is $\theta$. The horizontal surface is sufficiently rough to prevent slipping of prism. The body of mass $m$ is coming down the inclined face. Then

1. Acceleration of body along the inclined surface is $g\sin \theta$
2. Frictional force is $\frac{1}{2}mg\sin 2\theta$
3. Maximum frictional force is $\frac{mg}{2}$
4. Frictional force will be maximum when $\theta ={45}^{\circ }$

Q. For the arrangement shown in figure, the tension in the string to prevent it from sliding down is

1. $6\text{N}$
2. $64\text{N}$
3. $0.4\text{N}$
4. None of these

Q. In the shown arrangement if $f_1,f_2$ and $T$ be the frictional forces on $2\text{kg}$ block, $3\text{kg}$ block and tension in the string respectively, then their values are

1. $2\text{N},6\text{N},3.2\text{N}$
2. $2\text{N},6\text{N},0\text{N}$
3. $1\text{N},6\text{N},2\text{N}$
4. Data insufficient to calculate the required values

Q. A block of mass $10\text{kg}$ is pressed against a vertical wall. If the coefficient of friction between the wall and the block is $0.2$, then what is the minimum force that should be applied on the block so that does not fall to the ground?

1. $500\text{N}$
2. $400\text{N}$
3. $600\text{N}$
4. $555.5\text{N}$

Q. In the figure shown, if the block does not slide down the plane when a force of $\text{10 N}$ is applied perpendicular to the plane, find the coefficient of static friction between the plane and the block.(Consider limiting case of friction) Take $g={\text{10 m/s}}^2.$

1. $\frac{1}{\sqrt{2}}$
2. $\frac{1}{2}$
3. $\frac{1}{3}$
4. $\frac{1}{\sqrt{3}}$

Q. A piece of ice starting from rest slides down a rough ${45}^{\circ }$ incline in twice the time it takes to slide down a frictionless ${45}^{\circ }$ incline. What is the coefficient of friction between the ice and incline?

1. $0.25$
2. $0.50$
3. $0.75$
4. $0.40$

Q. Figure shows a block of mass $m$ placed on a horizontal surface. The coefficient of static friction between the block and the surface is $\mu$. The maximum force $F$ that can be applied at point $O$ such that the block does not slip on the surface is

1. $\mu mg\sin \theta$
2. $\mu mg\cos \theta$
3. $\mu mg\tan \theta$
4. $\mu mg$

Q. Two blocks $A$ and $B$ of mass $5\text{kg}$ and $2\text{kg}$, respectively, connected by a spring of force constant $=100\text{N/m}$ and are placed on an inclined plane of inclination ${30}^{\circ }$ as shown. If the system is released from rest then

1. There will be no compression or elongation in the spring, if all the surfaces are smooth.
2. There will be elongation in the spring, if $A$ is rough and $B$ is smooth.
3. Maximum elongation in the spring is $35\text{cm}$, if all surfaces are smooth.
4. There will be elongation in the spring, if $A$ is smooth and $B$ is rough.

Q. A car starts from rest to cover a distance $s$. The coefficient of friction between the road and the tyres is $\mu$. The minimum time in which the car can cover the distance is proportional to

1. $\mu$
2. $\sqrt{\mu }$
3. $\frac{1}{\mu }$
4. $\frac{1}{\sqrt{\mu }}$

Q. A block of mass $15\text{kg}$ is resting on a rough inclined plane as shown in figure. The block is tied up by a horizontal string which has a tension of $50\text{N}$. The coefficient of friction between the surfaces of contact is $(g=10{\text{m/s}}^2)$

1. $3/4$
2. $1/4$
3. $1/2$
4. $2/3$

Q. The brakes of a car moving at $20m/s$ along a horizontal road are suddenly applied and it comes to rest after travelling some distance. If the coefficient of friction between the tyres and the road is $0.90$, and it is assumed that all four tyres behave identically, find the shortest distance the car would travel before coming to a stop.

1. $2.22m$
2. $11.35m$
3. $22.2m$
4. $4.54m$

Q. Find the minimum value of $F$ for which the system is in equilibrium? $[$ Take $g={\text{10 m/s}}^2]$

1. $30\text{N}$
2. $10\text{N}$
3. $15\text{N}$
4. $20\text{N}$

Q. In the figure shown, what is the value of mass ‘$m$’ such that block $A$ slides up with a constant velocity. Take $g=10{\text{m/s}}^2$, Coefficient of friction between inclined plane and block $A$ is $0.5$.

1. $\text{1 kg}$
2. $\text{2 kg}$
3. $\text{3 kg}$
4. $\text{4 kg}$

Q. Find the minimum value of coefficient of friction between the $4\text{kg}$ block and the surface for the system to be at rest for the figure shown, (Block $A=4\text{kg}$ and block $B=3\text{kg}$)

1. $0.4$
2. $0.5$
3. $0.6$
4. $0.75$