Pure Rolling

Q.

The height above the Earth's surface at which the value of acceleration due to gravity reduces to half its value on the Earth's surface is h. Assume the Earth to be a sphere of radius 6400 Km. Find h.

1. 3650 km

2. 2650 km

3. 4650 km

4. 1650 km

Q.

A solid cylinder of mass $m$ is wrapped with an inextensible light string and is placed on a rough inclined plane as shown in the figure. The frictional force acting between the cylinder and the inclined plane is :

[The coefficient of static friction, ${\mu }_s$, is 0.4]

1. $72mg$

2. $0$

3. $mg/5$

4. $5mg$

Q.

The moment of inertia of two spheres of equal masses about their diameters is the same. One is hallow, then the ratio of their diameters is

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Q. 19.how to calculate the radius of curvature at the point of projection of the trajectory

Q. Two identical solid spheres each of radius R are kept at a dis†an ce of 2R (Centre to centre) from each other, then the gravitational force (F) between them depends on radius R as Options: a-R2 b- R4 c- R–2 d- R–4

Q.

In the absence of an external torque on a system, which of the following will not change?

1. linear momentum

2. angular momentum

3. moment of inertia

4. both i. and ii

Q. TWO BALLS ARE PROJECTED MAKING ANGLES OF 30 AND 45 DEGREE RESP WITH THE HORIZONTAL .IF THE BOTH HAVE SAME VELOCITY AT THE HIGHEST POINT OF THEIR PATH , THEN WHAT IS THE RATIO OF THEIR HORIZONTAL RANGES?

Q. Read each statement below carefully, and state, with reasons, if it is true or false; (a) During rolling, the force of friction acts in the same direction as the direction of motion of the CM of the body. (b) The instantaneous speed of the point of contact during rolling is zero. (c) The instantaneous acceleration of the point of contact during rolling is zero. (d) For perfect rolling motion, work done against friction is zero. (e) A wheel moving down a perfectly frictionless inclined plane will undergo slipping (not rolling) motion.

Q. 2. One end of a light spring of natural length d and spring constant k = mg/d is fixed on a rigid support and the other end is fixed to a smooth ring of mass M which can slide without friction on a vertical rod fixed at a distance d from the support . Initially , the spring makes an angle of 37 degree with the horizontal as shown in figure . The system is released from rest . What will beThe speed of the ring at the same angle subtended downward.

Q. Explain why friction is necessary to make the disc in Fig. 7.41 roll in the direction indicated. (a) Give the direction of frictional force at B, and the sense of frictional torque, before perfect rolling begins. (b) What is the force of friction after perfect rolling begins ?

Q.

The velocity of the centre of a smaller cylinder is $ v$. There is no slipping anywhere. The velocity of the center center of a larger cylinder is

Q. 30.Whatwill be the value of maximum acceleration of the truck in the forward direction so that blocks kept on the back does not topple

Q. Three balls A, B and C are kept in a straight line. The separation between A and C is 1 m, and B is placed at the midpoint between them. The masses of A, B, C are 100 g, 200g and 300g respectively. Find the net gravitational force on (a)A, (b)B, and (c)C.

Q.

The kinetic energy of a rolling wheel is

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Q. 90.A bob is attached to one end of a string other end of which is fixed at peg A. The bob is taken to a position where string makes an angle of 30 with the horizontal. On the circular path of the bob in vertical plane there is a peg B at a symmetrical position with respect to the position of release as shown in the figure. If Vc and Va be the minimum tangential velocity in clockwise and anticlockwise directions respectively, given to the bob in order to hit the peg B then ratio Vc : Va is equal to

Q. a uniform rod of lengt l and mass m is hinged at one end O and released from horizontal position as shown in figure the angular velocity o the rod as it passes the vertical positio

Q. 11.The angular velocity of a body changes from Omega 1 to Omega 2 without applying a torque but by changing the moment of inertia about its axis of rotation The ratio of its corresponding radius of gyration is

Q. Assertion hollow sphere is rollingdown on rough incline plane. Work done byfriction is zero. Reason No friction force acts on the sphere inabove case

Q. A ring of mass $m$ and radius $r$ is allowed to roll down without slipping on an inclined plane having inclination ${\sin }^{-1}\left(\frac{1}{10}\right)$ from the horizontal. The magnitude of acceleration of its centre of mass is

1. $9.8{\text{ms}}^{-2}$
2. $4.9{\text{ms}}^{-2}$
3. $0.98{\text{ms}}^{-2}$
4. $0.49{\text{ms}}^{-2}$

Q. Two identical uniform discs roll without slipping on two different surfaces as shown in figure. If they reach points $B$ and $D$ with the same linear speed, then $v_2$ (in $\text{m/s}$) is
[Take $g=10{\text{m/s}}^2$]

Q. 53.derivation of equations of motion by all method

Q.

When an object rotates about a fixed point, then this fixed point is called the ______ of rotation.

Q. If three uniform spheres, each having mass $M$ and radius $R$, are kept in such a way that each touch the other two, the magnitude of the gravitational force on any sphere due to the other two is

1. $\frac{2G{M}^2}{R^2}$
2. $\frac{2G{M}^2}{4R^2}$
3. $\frac{G{M}^2}{4R^2}$
4. $\frac{\sqrt{3}G{M}^2}{4R^2}$

Q. A solid uniform cylinder of mass $M$ and radius $R$ is pivoted at its centre free to rotate about horizontal axis. A massless inextensible string is wrapped around it, and attached to a block of mass $m$ which is initially at a height $h$ above the floor. The acceleration due to gravity is $g$, directed downward. The block is released from rest. By what total angle $\theta$ does it rotate (in radians)?

1. $\sqrt{1+\frac{2M}{m}}$
2. $\frac{h}{R}$
3. $\sqrt{1+\frac{h}{2R}}$
4. $\frac{MR}{mh}$

Q. Three uniform spheres each having mass m and radiusR kept in such a way that each thouches the other.the magnitude of the gravitational force on any sphere due to the other cases

Q. A solid sphere, a hollow sphere and a disc, all having same mass and radius, are placed at the top on an incline and released. The friction coefficients between the objects and the incline are same and not sufficient to allow pure rolling. Least time will be taken in reaching the bottom by
(a) the solid sphere
(b) the hollow sphere
(c) the disc
(d) all will take same time.

Q.

How is net torque related to angular acceleration?

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Q. A solid sphere of radius $R$ is resting on a smooth horizontal surface. A constant force $F$ is applied at a height $h$ from the bottom. Choose the correct alternative

1. Sphere will always slide whatever be the value of $h$
2. Sphere will roll without slipping when $h\ge 1.4R$
3. Sphere will roll without slipping if $h=1.4R$
4. None of the above

Q. Two identical balls, each of radius R are kept in contact. The gravitational force between them is proportional to Options: (a) R (b)R^2 (c)R^{-4} (d)R^4 Correct= R^4 how?

Q. A solid cylinder of mass $M$ and radius $R$ rolls down an inclined plane of height $h$. The angular velocity of the cylinder when it reaches the bottom of the plane will be

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