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

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) (1/2)mv2 (B) (5/3)mv2 (C) (2/5)mv2 (D) (7/10)mv2

Tardigrade Admin · Accepted Answer

Take KE at bottom KE =(1/2) m v2[1+(K2/R2)] =(1/2) m v2[1+(2/5)] =(7/10) m v2

Q. 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

$\frac{1}{2} m v^{2}$

$\frac{5}{3} m v^{2}$

$\frac{2}{5} m v^{2}$

$\frac{7}{10} m v^{2}$

Take KE at bottom
$K E = \frac{1}{2} m v^{2} [1 + \frac{K ^{2}}{R ^{2}}]$
$= \frac{1}{2} m v^{2} [1 + \frac{2}{5}]$
$= \frac{7}{10} m v^{2}$

Q. 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

21​mv2

35​mv2

52​mv2

107​mv2