Question:
A solid sphere of mass $m$ rolls down an inclined plane without slipping, starting from rest at the top of an inclined plane. The linear speed of the sphere at the bottom of the inclined plane is $v$. The kinetic energy of the sphere at the bottom is
A solid sphere of mass $m$ rolls down an inclined plane without slipping, starting from rest at the top of an inclined plane. The linear speed of the sphere at the bottom of the inclined plane is $v$. The kinetic energy of the sphere at the bottom is
Updated On: May 30, 2022
- $\frac{1}{2}mv^{2}$
- $\frac{5}{3}mv^{2}$
- $\frac{2}{5}mv^{2}$
- $\frac{7}{10}mv^{2}$
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The Correct Option is D
Solution and Explanation
Take KE at bottom
$KE =\frac{1}{2} m v^{2}\left[1+\frac{K^{2}}{R^{2}}\right]$
$=\frac{1}{2} m v^{2}\left[1+\frac{2}{5}\right]$
$=\frac{7}{10} m v^{2}$
$KE =\frac{1}{2} m v^{2}\left[1+\frac{K^{2}}{R^{2}}\right]$
$=\frac{1}{2} m v^{2}\left[1+\frac{2}{5}\right]$
$=\frac{7}{10} m v^{2}$
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Concepts Used:
System of Particles and Rotational Motion
- The system of particles refers to the extended body which is considered a rigid body most of the time for simple or easy understanding. A rigid body is a body with a perfectly definite and unchangeable shape.
- The distance between the pair of particles in such a body does not replace or alter. Rotational motion can be described as the motion of a rigid body originates in such a manner that all of its particles move in a circle about an axis with a common angular velocity.
- The few common examples of rotational motion are the motion of the blade of a windmill and periodic motion.