Direction of Friction

Q. A solid sphere of mass 2 kg rolls on a smooth horizontal surface at 10 m/s. It then rolls up a smooth inclined plane of inclination ${30}^{\circ }$. Height attained by sphere in meter before stopping is: (take $g=10{\text{ms}}^{-2}$)

Q. A disk and a sphere of same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first?

1. Disk
2. Depends on their masses
3. Sphere
4. Both reach at the same time.

Q. A solid sphere of Mass $M$ and radius $R$ is pulled horizontally on a rough surface as shown in the figure. Choose the incorrect alternative(s).

1. The magnitude of the frictional force is $F/3$.
2. The frictional force on the sphere acts forward.
3. The acceleration of the centre of mass is $2F/3M$.
4. The acceleration of the centre of mass is $5F/7M$.

Q. A long cylindrical vessel is half filled with a liquid. When the vessel is rotated about its own vertical axis, the liquid rises up near the wall. If the radius of the vessel is $5\text{cm}$ and its rotational speed is $2$ rotations per second, then the difference in the heights between the centre and the sides, $\text{in cm}$, will be:

1. $2.0$
2. $1.2$
3. $0.1$
4. $0.4$

Q. A horizontal disc rotates freely about a vertical axis through its centre. A ring having the same mass and radius as the disc, is now gently placed on the disc. After some time, the two rotate with a common angular velocity, then

1. some friction exists between the disc and the ring
2. the angular momentum of the 'disc plus ring' is conserved
3. The final common angular velocity is ${\left(\frac{2}{3}\right)}^{rd}$ of the initial angular velocity of the disc
4. ${\left(\frac{2}{3}\right)}^{rd}$ of the initial kinetic energy changes to heat

Q. A thin ring of mass $2\text{kg}$ and radius $1\text{m}$ is rolling without slipping on a horizontal plane with velocity $1\text{m/s}$. A small ball of mass $1\text{kg}$ and moving with velocity $2\text{m/s}$ in the opposite direction, hits the ring at a height of $1.8\text{m}$ and goes vertically up with velocity of $1\text{m/s}$. Immediately after the collision, which of the following is true?

1. Ring undergoes pure rotation about its axis through the centre of mass.
2. Ring comes to a complete stop.
3. Friction on the ring by the ground is to the left.
4. There is no friction between the ring and ground.

Q. Two balls of same mass are projected with the same speed one vertically upwards and the other at angle ${60}^{\circ }$ with the vertical. The ratio of their potential energy at the highest point is

1. 4 : 1
2. 2 : 1
3. 3 : 2
4. 4 : 3

Q. A uniform disk of mass m and radius R is projected horizontally with velocity $V_0$ on a rough horizontal floor so that it starts off with a purely sliding motion at t = 0. After $t_0$ seconds, it acquires a purely rolling motion as shown in figure.

1. Angular momentum of disc at t = 0 about a point on the floor and in the same plane which contains the disc is $m{V}_{0}R$.
2. Angular momentum of disc at $t=t_0$ about a point on the floor and in the same plane which contains the disc is $m{V}_{0}R$.
3. Speed of the centre of mass of disc at $t=t_0$ is $2V_0/3$
4. Speed of the centre of mass of disc at $t=t_0$ is $3V_0/4$

Q.

A cylinder rolls on a horizontal plane surface. If the speed of the centre is 25 m/s, what is the speed of the highest point ?

Q. A solid sphere (mass 2 M) and a thin spherical shell (mass M) both of the same size, roll down an inclined plane, then

1. Hollow spherical shell will reach the bottom first
2. Both will reach at the same time
3. Cannot be predicted as the data is insufficient
4. Solid sphere will reach the bottom first
5. None of the above

Q. The frictional force on the ring (as shown in figure) is

1. $\frac{F}{3}$ towards left
2. $\frac{2F}{3}$ towards left
3. Zero
4. $\frac{F}{3}$ towards right

Q. Find the velocity of a satellite travelling in an elliptical orbit, when it reaches point $\text{C}$ on the end of the semi-minor axis.

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

Q. Two forces of magnitude $F$ each are acting on a uniform disc kept on a horizontal surface as shown in the figure. The disc performs rolling without slipping. If the frictional force by the horizontal surface is $nF$. The value of $n$ is

Q. What is the frictional force acting on the block as shown in the figure?

1. $10N$
   
2. $0N$
3. $5N$
4. Can't say until $\mu$ is not given.

Q. A ball rolls down an inclined plane and acquires a velocity $v_r,$ when it reaches the bottom of the plane. If the same ball slides from the same height on smooth inclined plane and acquires a velocity $v_B$ at bottom. Which of the following statements is/are incorrect?

1. $v_r<v_s$, because some work is done by the rolling ball against the frictional force.
2. $v_r>v_s$. because the angular velocity acquired makes the rolling ball to travel faster
3. $v_r=v_s$, because kinetic energy of two balls is same at bottom of planes
4. $v_r<v_s$, because the rolling ball acquires rotational as well as translational kinetic energy

Q.

Comprehension Type: A uniform thin cylindrical disk of mass M ad radius R is attached to two identical mass less springs of springs constant k which are fixed to the wall as show in the figure. The springs are attached to the axle of the disk symmetrically on either side at a distance d from its center. The axle is mass less and both the springs and the axle are in horizontal plane. The un-stretched length of each springs is L. The disk is initially at its equilibrium position with its center of mass (CM) at a distance L from the wall. The disk rolls without slipping with velocity $\overrightarrow{(}V{)}_0=V_0\hat{i}$ The coefficient of friction is $\mu$.

The net external force acting on the disk when its centre of mass is at displacement x with respect to its equilibrium position is

1. - kx

2. - 2kx

3. 

4. 

Q. A disc of mass $M$ and radius $R$ rolls on a horizontal surface and then rolls up an inclined plane as shown in figure. If the velocity of the disc is $v$, height to which the disc will rise will be

1. $\frac{3v^2}{2g}$
2. $\frac{3v^2}{4g}$
3. $\frac{v^2}{4g}$
4. $\frac{v^2}{2g}$

Q. A horizontal plane supports a fixed vertical cylinder of radius R and a particle is attached to the cylinder by a horizontal thread AB as shown in figure. A horizontal velocity $V_0$ is imparted to the particle, normal to the thread, during subsequent motion–

1. Angular momentum of particle about O remains constant
2. Angular momentum about B remains constant
3. Momentum and kinetic energy both remain constant
4. Kinetic energy alone remains constant

Q. A uniform sphere of mass ${}^{\prime }{m}^{\prime }$ is given some angular velocity about a horizontal axis through its centre and gently placed on a plank of mass ${}^{\prime }{m}^{\prime }$. The co-efficient of friction between the two is $\mu$. The plank rests on a smooth horizontal surface. The initial acceleration of the centre of the sphere relative to the plank will be:

1. zero
2. $2\mu g$
3. $\mu g$
4. $\left(\frac{7}{5}\right)\mu g$

Q.

A small ball starts rolling on a inclined track with becomes loop if radius R in vertical plane.

1. Speed of the ball at highest point is zero but and highest point is 2R above the ground.

2. Speed of the ball at highest point is non zero but highest point is 2R above the ground

3. Speed of the ball is along horizontal at highest point and highest point is less than the 2R above the ground.

4. Speed of the ball is along horizontal at highest point but height of highest point above the around can not be calculated.

Q. A ball is rolling on ice with velocity of 4.9m/s, stop after travelling 4m.What is the coefficient of friction

Q. Two rods of same mass and same length $l_0$ but having different coefficient of expansions $\alpha$ and $3\alpha$ are joined at P (see figure). System is placed on frictionless surface. If temperature of whole system is changed by $△T,$ the displacement of junction point is

1. $l_0\alpha △T$
   
2. $2l_0\alpha △T$
   
3. $\frac{3}{4}{l}_0\alpha △T$
4. $\frac{l_0\alpha △T}{2}$
   

Q. Assertion :A rigid disc rolls without slipping on a fixed rough horizontal surface with uniform angular velocity. Then the acceleration of lowest point on the disc is zero. Reason: For a rigid disc rolling without slipping on a fixed rough horizontal surface, the velocity of the lowest point on the disc is always zero.

1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
2. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
3. Assertion is correct but Reason is incorrect
4. Assertion is incorrect but Reason is correct

Q. A solid sphere of mass $m$ and radius $R$ is gently placed on a conveyer belt moving with constant velocity $V_0$. If coefficient of friction between belt and sphere is $2/7$, the distance travelled by the centre of the sphere before it starts pure rolling is

1. $\frac{V_0^2}{7g}$
   
2. $\frac{2V_0^2}{7g}$
3. $\frac{2V_0^2}{5g}$
4. $\frac{2V_0^2}{49g}$

Q. A car is moving along a straight horizontal road with speed $v_0$. If the coefficient of friction between the tyres and the road is $\mu$, the shortest distance in which the car can be stopped is

1. $\frac{v_0}{\mu }$
2. $\frac{v_0}{\mu g}$
3. $\frac{v_0^2}{2\mu g}$
4. $(\frac{v_0}{\mu g}{)}^2$

Q. Two discs of moment of inertia $I_1$ and $I_2$ about their respective axes which are passing through centre and perpendicular to surface, rotating with angular frequencies ${\omega }_1$ and ${\omega }_2$ respectively, are brought into contact face to face with their axes of rotation coincident. The angular frequency of the composite disc will be

1. $\frac{I_1{\omega }_1-I_2{\omega }_2}{I_1-I_2}$
2. $\frac{I_1{\omega }_1+I_2{\omega }_2}{I_1+I_2}$
3. $\frac{I_2{\omega }_1+I_1{\omega }_2}{I_1+I_2}$
4. $\frac{I_2{\omega }_1-I_1{\omega }_2}{I_1-I_2}$

Q. A car is moving along a straight horizontal road with speed $v_0$. If the coefficient of friction between the tyres and the road is $\mu$, the shortest distance in which the car can be stopped is

1. $\frac{v_0^2}{2\mu g}$
2. $\frac{v_0}{\mu g}$
3. $(\frac{v_0}{\mu g}{)}^2$
4. $\frac{v_0}{\mu }$

Q. A solid sphere of Mass $M$ and radius $R$ is pulled horizontally on a rough surface as shown in the figure. Choose the incorrect alternative(s).

1. The magnitude of the frictional force is $F/3$.
2. The frictional force on the sphere acts forward.
3. The acceleration of the centre of mass is $2F/3M$.
4. The acceleration of the centre of mass is $5F/7M$.

Q. A disc of circumference s is at rest at a point A on a horizontal surface when a constant horizontal force towards right begins to act on its centre. Between A and B on the horizontal surface there is sufficient friction to prevent slipping and the surface is smooth to the right of B, AB =s . The disc moves from A to B in time T. To the right of B:

1. The angular acceleration of the disc will disappear, linear acceleration will remain unchanged
2. Linear acceleration of the disc will increase
3. The disc will make one rotation in time $\frac{T}{2}$
4. The disc will cover a distance greater than s in further time T

Q.

A rigid body of mass 'M' and radius R is rolling without sliding, along with bock of radius of gyration K, and mass $m_1$, then find the minimum value of friction coefficient $\mu$?

1. $\frac{M{k}^2}{R^2\{M+m(1+\frac{k^2}{R^2}\left)\right\}}$

2. $\frac{M{k}^2}{R^2\{M+m(1+\frac{k^2}{R^2}\left)\right\}}$

3. $\frac{M{R}^2}{k^2\{M+m(1+\frac{k^2}{R^2}\left)\right\}}$

4. $\frac{M{R}^2}{k^2\{M+m(1+\frac{k^2}{R^2}\left)\right\}}$