Slipping

Q. A rod of length $50\text{cm}$ is pivoted at one end. It is raised such that if makes an angle of ${30}^{\circ }$ from the horizontal as shown and released from rest. Its angular speed when it passes through the horizontal (in ${\text{rad s}}^{-1}$) will be ($g=10{\text{m s}}^{-2}$)

1. $\frac{30}{2}$
2. $\sqrt{\frac{30}{7}}$
3. $\sqrt{\frac{20}{3}}$
4. $\sqrt{30}$

Q.

A sphere of mass M and radius r shown in figure slips on a rough horizontal plane. At some instant it has translational velocity $v_0$ and rotational velocity about the centre $\frac{v_0}{2r}$. Find the translational velocity after the sphere starts pure rolling.

1. 2v₀

2. 

3. v₀

4. 

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

Q. A uniform ring placed on a rough horizontal surface is given a sharp impulse as shown in the figure. As a consequence, it acquires a linear velocity of $2\text{m/s}$. If coefficient of friction between the ring and the horizontal surface is 0.4, then:

1. Ring will start rolling after 0.25 s
2. When ring starts pure rolling, its velocity is $1\text{m/s}$
3. After 0.5 s from impulse, its velocity is $1\text{m/s}$
4. After 0.125 s from impulse, its velocity is $1\text{m/s}$.

Q.

A ball falls on an inclined plane of inclination $\theta$ from a height h above the point of impact and makes a perfectly elastic collision.Where will it hit the plane again ?

Q. A sphere cannot roll without slipping on a

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

Q.

A thick walled hollow sphere has outer radius R. It rolls down an inclined plain Without slipping and its speed at the bottom is v. If the inclined plane is frictionless and the sphere slides down without rolling, its speed at the bottom will be 5v/4. What is radius of gyration of the sphere.

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. None of these

2. 

3. 

4. 

Q. The figure shows three rotating, uniform discs that are coupled by belts. One belt runs around the rims of discs $A$ and $C$. Another belt runs around a central hub on the disc $A$ and the rim of the disc $B$. The belts move smoothly without slippage on the rims and hub. Disc $A$ has radius $R$; its hub has radius $0.500R$; disc $B$ has radius $0.250R$ and disc $C$ has radius $2.00R$. Discs $B$ and $C$ have the same density $($mass per unit volume$)$ and thickness. What is the ratio of the magnitude of the angular momentum of the disc $C$ to that of the disc $B$ ?

1. $1224:1$
2. $1024:1$
3. $1424:1$
4. $1624:1$

Q. Why A tennis ball Bounces higher on the Hills than in plains

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 projected up on an inclined plane with a velocity $v_o$ and angular velocity as shown. The coefficient of friction between the sphere and the plane is $\mu =tan\theta$. Find the total time of rise of the sphere.

1. $\frac{v_o}{gsin\theta }$
2. $\frac{7v_o}{9gsin\theta }$
3. $\frac{2v_o}{9gsin\theta }$
4. $\frac{7v_o}{2gsin\theta }$

Q.

A billiard ball (of radius R), initially at rest is given a harp impulse by a cue. The cue is held horizontally a distance h above the central line. The ball leaves the cue with a speed $V_0$, eventually acquires a final speed of $\frac{9}{7}{V}_0$. Find h.

1. None of these

2. 7R/13

3. 2R/3

4. 4R/5

Q. A disc is rotated about its axis with a certain angular velocity and lowered gently onto an inclined plane as shown in the figure. Then,

1. It will go downwards just after it is placed.
2. It will move downwards first and then climb up along the inclined plane.
3. It will climb upwards along the inclined plane and then move downwards.
4. It will rotate at the position where it was placed and then will move downwards.

Q.

A bowling ball is thrown down the alley in such a way that it slides with a speed $v_0$ initially without rolling. What will it its speed be when (and if) it starts pure rolling? The transition from pure sliding to pure rolling is gradual, so that both sliding and rolling takes place during this interval.

1. none of these

2. 

3. 

4. 

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 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. Friction is acting forward along plane
4. Cylinder is in pure rolling

Q. A sphere of mass M and radius R is released from the top of an inclined plane of inclination $\theta$. The minimum coefficient of friction between the plane and the sphere so that it rolls down the plane without sliding is given by

1. $\mu =tan\theta$
2. $\mu =\frac{2}{3}tan\theta$
3. $\mu =\frac{2}{5}tan\theta$
4. $\mu =\frac{2}{7}tan\theta$

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. 2.5 sec

2. 2.25 sec

3. 2 sec

4. 3 sec

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. backwards
2. forwards
3. zero
4. \N

Q. A horizontal F is applied on a spherical shell of radius R at distance R/2 above center as shown in figure. Shell is doing pure rolling motion and friction acting on it is $f=\frac{xF}{y}$ then, y-x is

Q.

A block sliding down a rough 45° inclined plane has half the velocity it would have had , the inclined plane been smooth .the coefficient of sliding friction between block and inclined plane is???

Q. A uniform disc of mass $m$ and radius $R$ is placed on a smooth horizontal surface. An impulse $I$ is given horizontally to the sphere at height $h=\frac{3R}{5}$ above the centre line. Then which of the following option is incorrect?

1. The minimum time after which the highest point touches the ground is $\frac{\pi Rm}{2I}$
2. The minimum time after which the highest point touches the ground is $\frac{5\pi Rm}{6I}$
3. The displacement of the COM during this interval is $\frac{5\pi R}{6}$
4. None of these

Q. A solid sphere of mass m is placed on rough inclined plane as shown in figure. Friction is sufficient to allow pure rolling. Work done by friction, when sphere traverse a distance l along the incline, is


of

Q. In order to survive a road accident, the vehicle is stopped suddenly such that the translational distance covered by the wheel is much greater than its angular displacement. This is an example of

1. forward slipping
2. backward slipping
3. pure rolling
4. all of the above

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. ω₀< v₀/R

2. ω₀> v₀/R

3. It will never return back

4. ω₀ = μv₀/R

Q.

A bowling ball is thrown down the alley in such a way that it slides with a speed $v_0$ initially without rolling. What will it it's speed be when (and if) it starts pure rolling? The transition from pure sliding to pure rolling is gradual, so that both sliding and rolling takes place during this interval.

1. $\frac{5}{7}{v}_0$

2. $\frac{2}{3}{v}_0$

3. $\frac{5}{12}{v}_0$

4. None of these

Q. Diagram shows the top-view of an annular disc of mass $8\text{kg}$ that can freely rotate about its centre. With a cat of mass $2\text{kg}$ on its outer edge, it is initially rotating at an angular speed of $8\text{rad/s}$. What will be the increase in kinetic energy of the cat $\&$ ring system, if cat finally reaches to the inner edge.

1. $25\text{J}$
2. $80\text{J}$
3. $10\text{J}$
4. $39\text{J}$

Q.

A bowling ball is thrown down the alley in such a way that it slides with a speed $v_0$ initially without rolling. What will it its speed be when (and if) it starts pure rolling? The transition from pure sliding to pure rolling is gradual, so that both sliding and rolling takes place during this interval.

1. 

2. 

3. None of these

4. 

Q. A cylinder of mass $10$kg is sliding on a plane with an initial velocity of $10$m/s. If coefficient of friction between surface and cylinder is $0.5$, then before stopping it will travel a distance of:

1. $5$ m
2. $10$ m
3. $7.5$ m
4. $12.5$ m