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(A) The acceleration of a body rolling down an inclined plane is given by $a = \frac{g \sin 	heta}{1 + \frac{I}{mR^2}}$.The moment of inertia $I$ for

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The sphere has the greatest and the ring has the least velocity of the centre of mass at the bottom of the inclined plane.

Vedclass · Answer

(A) The acceleration of a body rolling down an inclined plane is given by $a = \frac{g \sin 	heta}{1 + \frac{I}{mR^2}}$.The moment of inertia $I$ for the objects are: $I_{	ext{ring}} = mR^2$,$I_{	ext{cylinder}} = \frac{1}{2}mR^2$,and $I_{	ext{sphere}} = \frac{2}{5}mR^2$.Comparing the moments of inertia: $I_{	ext{ring}} > I_{	ext{cylinder}} > I_{	ext{sphere}}$.Since $a$ is inversely proportional to the factor $(1 + \frac{I}{mR^2})$,the acceleration follows the order: $a_{	ext{ring}} Using the kinematic equation $v^2 = u^2 + 2as$ with $u = 0$,the final velocity $v = \sqrt{2as}$ is directly proportional to the square root of acceleration.Therefore,the final velocities at the bottom of the plane follow the order: $v_{	ext{ring}} Thus,the sphere has the greatest velocity and the ring has the least velocity.

Consider a situation in which a ring,a solid cylinder,and a solid sphere roll down on the same inclined plane without slipping. Assume that they start rolling from rest and have identical diameters. The correct statement for this situation is:

Similar Questions

$A$ solid cylinder rolls up an inclined plane of angle of inclination $30^{\circ}$. At the bottom of the inclined plane,the centre of mass of the cylinder has a speed of $5 \; m/s$.
$(a)$ How far will the cylinder go up the plane?
$(b)$ How long will it take to return to the bottom?

$Assertion$ : The velocity of a body at the bottom of an inclined plane of given height is more when it slides down the plane,compared to when it rolls down the same plane.
$Reason$ : In rolling down,a body acquires both kinetic energy of translation and rotation.

$A$ spherical uniform body of radius $R$,mass $M$,and moment of inertia $I$ rolls down (without slipping) on an inclined plane making an angle $\theta$ with the horizontal. Then its acceleration is

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