Slipping

Q. A solid cylinder rolling down on an inclined plane as shown in figure. Which of the following options correctly depicts the motion of cylinder on the inclined plane?

1. Cylinder is slipping forward
2. Cylinder is slipping backward
3. Cylinder is in pure rolling
4. Friction is acting forward along plane

Q. A sphere cannot roll without slipping on a

1. rough horizontal surface
2. horizontal surface (rough or smooth)
3. rough inclined surface
4. smooth inclined surface

Q. A constant force $F$ acts tangentially at the highest point of a uniform disc of mass $m$ kept on a rough horizontal surface as shown in figure. If the disc rolls without slipping, calculate the acceleration of the centre $C$ and points $A$ and $B$ on the disc.

1. $a_C=\frac{4F}{3m},a_A=0,a_B=\frac{8F}{3m}$
2. $a_C=\frac{2F}{3m},a_A=0,a_B=\frac{4F}{3m}$
3. $a_C=\frac{F}{m},a_A=0,a_B=\frac{2F}{3m}$
4. $a_C=\frac{F}{2m},a_A=0,a_B=\frac{F}{2m}$

Q. A sphere is resting on a horizontal surface with friction and starts rotating clockwise. A force of 15 N is applied on it as shown. What is the direction of frictional force on the sphere?

1. forwards
2. backwards
3. frictional force is not getting applied
4. can not be determined

Q. A solid cylinder of mass $m$ is kept on the edge of a plank of mass $3m$ and length $15\text{m}$ which in turn is kept on smooth ground. The coefficient of friction between the plank and the cylinder is $0.1$. The cylinder is given an impulse which imparts it a velocity of $6\text{m/s}$ but no angular velocity. Find the time (jn seconds) after which the cylinder will start pure rolling.

Q. A hoop of radius r and mass m rotating with an angular velocity ${\omega }_0$ is placed on a rough horizontal surface. The initial velocity of the centre of the hoop is zero. What will be the velocity of the centre of the hoop when it ceases to slip?

1. $\frac{r{\omega }_0}{3}$
2. $\frac{r{\omega }_0}{2}$
3. $r{\omega }_0$
4. $\frac{r{\omega }_0}{4}$

Q. A sphere is resting on a horizontal surface with friction and starts rotating clockwise. A force of 15 N is applied on it as shown. What is the direction of frictional force on the sphere?

1. forwards
2. backwards
3. frictional force is not getting applied
4. can not be determined

Q. A hoop of radius r and mass m rotating with an angular velocity ${\omega }_0$ is placed on a rough horizontal surface. The initial velocity of the centre of the hoop is zero. What will be the velocity of the centre of the hoop when it ceases to slip?

1. $\frac{r{\omega }_0}{3}$
2. $\frac{r{\omega }_0}{2}$
3. $r{\omega }_0$
4. $\frac{r{\omega }_0}{4}$

Q.

A solid sphere of radius R is set into motion on a rough horizontal surface with a linear speed $v_0$ in forward direction ad an angular velocity ${\omega }_0=\frac{v_0}{2R}$ in counter clockwise direction as shown in figure. If co-efficient of friction is $\mu$, then find

(i)The time after which sphere starts pure rolling,

(ii)The work done by friction over a long time

1. $t=\frac{2}{17}\frac{v_0}{mug},W=\frac{-5}{13}m{v}_0^2$

2. $t=\frac{3v_0}{7mug},W=\frac{-9}{28}m{v}_0^2$

3. $t=\frac{7}{19}\frac{v_0}{mug},W=-3m{v}_0^2$

4. None of these

Q. A solid cylinder rolling down on an inclined plane as shown in figure. Which of the following options correctly depicts the motion of cylinder on the inclined plane?

1. Cylinder is slipping forward
2. Cylinder is slipping backward
3. Cylinder is in pure rolling
4. Friction is acting forward along plane

Q.

A cylinder of mass 'm; is kept on the edge of a plank of mass '2m' and length 12 metre, which in turn is kept on smooth ground. Coefficient of friction between the plank and the cylinder is 0.1. The cylinder is given an impulse, which imparts it a velocity 7 m/s but no angular velocity. Find the time after which the cylinder falls off the plank.

1. 2 sec
2. 3 sec
3. 2.5 sec
4. 2.25 sec

Q. A wheel of bicycle is rolling without slipping on a level road. If the velocity of the center of mass is $v_{cm}$, then true statement is

1. the velocity of point $A$ is $2v_{cm}$ and velocity of point $B$ is zero
2. the velocity of point $A$ is zero and velocity of point B is $2v_{cm}$
3. the velocity of point $A$ is $2v_{cm}$ and velocity of point $B$ is $-v_{cm}$
4. the velocities of both $A$ and $B$ are $v_{cm}$

Q.

A solid sphere of radius R is set into motion on a rough horizontal surface with a linear speed $v_0$ in forward direction ad an angular velocity ${\omega }_0=\frac{v_0}{2R}$ in counter clockwise direction as shown in figure. If co-efficient of friction is $\mu$, then find

(i)The time after which sphere starts pure rolling,

(ii)The work done by friction over a long time

1. $t=\frac{2}{17}\frac{v_0}{mug},W=\frac{-5}{13}m{v}_0^2$

2. $t=\frac{3v_0}{7mug},W=\frac{-9}{28}m{v}_0^2$

3. $t=\frac{7}{19}\frac{v_0}{mug},W=-3m{v}_0^2$

4. None of these

Q. This body is in ___

1. Pure rolling
2. Forward slipping
3. Backward slipping
4. Pure rotation

Q.

A hoop of mass 'm' and radius 'R' is projected on a floor with linear velocity $v_0$ and reverse spin ${\omega }_0$. The coefficient of friction between the hoop and the ground is $\mu$. Under what of the following condition will the hoop return back?

1. ${\omega }_0<\frac{v_0}{R}$

2. ${\omega }_0>\frac{v_0}{R}$

3. ${\omega }_0=\frac{\mu v_0}{R}$

4. It will never return back