Slipping

Q. 1.A small ball of mass m, radius r is released from rest from point 1 to roll inside a hemisphrical shell of radius R, as shown in the figure. The angularvelocity of the centre of the ball in point 2 about the centre of shell is

Q. A sphere rolling on horizontal surface starts moving up a rough inclined plane. If sphere rolls without slipping, then the frictional force on sphere is acting

1. Is zero
2. In downward direction along inclined plane
3. In vertically upward direction
4. In upward direction along inclined plane

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 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. $2v_0$

2. $\frac{5}{2}{v}_0$

3. $v_0$

4. $\frac{6}{7}{v}_0$

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

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. $\frac{7R}{13}$

2. $\frac{2R}{13}$

3. $\frac{4R}{13}$

4. None of these

Q. A solid sphere of mass 0⋅50 kg is kept on a horizontal surface. The coefficient of static friction between the surfaces in contact is 2/7. What maximum force can be applied at the highest point in the horizontal direction so that the sphere does not slip on the surface?

Q. is friction necessary for a body to roll? what is the minimum friction required for a disc of mass M and radius r to roll in an inclined plane

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

Q. A solid cylinder having radius 0.4 m, initially rotating (at t = 0) with ${\omega }_0$ = 54 rad/sec is placed on a rough inclined plane with $\theta ={37}^0$ having friction coefficient $\mu$ = 0.5. The time taken by the cylinder to start pure rolling is:

1. 1.8 sec
2. 5.4 sec
3. 1.4 sec
4. 1.2 sec

Q. Kindly Explain in detail Two spherical rain drops with radii in the ratio 1:2 fall with a constant velocity in atmosphere. The ratio of their linear momenta in this situation is

Q. the powder of subs†an ce is stored in conical heap of a cicular area π r^{2 }. if coeficient of static friction between powder particle of subs†an ce is μ. then maximum height of conical heap is

Q. A block of mass m is kept on a horizontal ruler. The friction coefficient between the ruler and the block is μ. The ruler is fixed at one end and the block is at a distance L from the fixed end. The ruler is rotated about the fixed end in the horizontal plane through the fixed end. (a) What can the maximum angular speed be for which the block does not slip? (b) If the angular speed of the ruler is uniformly increased from zero at an angular acceleration α, at what angular speed will the block slip?

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. $\frac{7R}{13}$

2. $\frac{2R}{13}$

3. $\frac{4R}{13}$

4. None of these

Q. A solid cylinder of mass 'm' rolls without slippling down an inclined plane making an angle $\theta$ with the horizontal. The frictional force between the cylinder and the incline is

1. mg sin $\theta$
2. $\frac{mgsin\theta }{3}$
3. mg cos $\theta$
4. $\frac{2mgsin\theta }{3}$