Assertion : The velocity of a body at the bot | vedclass

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Question

(A) When a body slides down an inclined plane of height $h$,the entire potential energy $mgh$ is converted into translational kinetic energy $\frac{1}

Vedclass · Accepted Answer

If both $Assertion$ and $Reason$ are correct and the $Reason$ is a correct explanation of the $Assertion$.

Vedclass · Answer

(A) When a body slides down an inclined plane of height $h$,the entire potential energy $mgh$ is converted into translational kinetic energy $\frac{1}{2}mv^2$. Thus,$v_{slide} = \sqrt{2gh}$.When a body rolls down the same plane,the potential energy $mgh$ is converted into both translational kinetic energy $\frac{1}{2}mv^2$ and rotational kinetic energy $\frac{1}{2}I\omega^2$. Thus,$mgh = \frac{1}{2}mv^2 + \frac{1}{2}I\omega^2$.Since some energy is used for rotation,the translational kinetic energy is less in the rolling case compared to the sliding case.Consequently,the linear velocity at the bottom is lower for rolling than for sliding.Therefore,both $Assertion$ and $Reason$ are correct,and the $Reason$ correctly explains the $Assertion$.

$Assertion$ : 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.

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$Assertion$ : 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.