Q. A marble and a cube have the same mass starting from rest, the marble rolls and the cube slides down a frictionless ramp. When they arrive at the bottom, the ratio of speed of the cube to the centre of mass and speed of the marble is
A) 7 : 5
B) $\sqrt{7}:\sqrt{5}$
C) $\sqrt{2}:1$
D) 5 : 2
Explanation
(b) If $h$ is height of the ramp, then in rolling of marble, speed
$v = \sqrt{\frac{2gh}{1 + K^{2}/R^{2}}}$
The speed of the cube to the centre of mass
$v^{'} = \sqrt{2gh}$
$\therefore\ \frac{v^{'}}{v} = \sqrt{1 + K^{2}/R^{2}}$
For marble sphere, $K^{2} = \frac{2}{5}R^{2}$
$\therefore\ \frac{v^{'}}{v} = \sqrt{1 + \frac{2}{5}} = \sqrt{\frac{7}{5}} = \sqrt{7}:\sqrt{5}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.