Consider a situation in which a ring, a solid cylinder and a soli… - Vidyadip

MCQ

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 having identical diameter.

The correct statement for this situation is:-

✓
The sphere has the greatest and the ring has the least velocity of the centre of mass at the bottom of the inclined plane.
B
The ring has the greatest and the cylinder has the least velocity of the centre of mass at the bottom of the inclined plane.
C
All of them will have same velocity.
D
The cylinder has the greatest and the sphere has the least velocity of the centre of mass at the bottom of the inclined plane.

✓

Answer

Correct option: A.

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

a
$a=\frac{g \sin \theta}{1+\frac{I}{m R^{2}}}$

$I_{\text {ring }}\,>\,I_{\text {solid cylinder }}\,>\,I_{\text {solid sphere }}$

$\Rightarrow a_{\text {ring }}\,<\,a_{\text {solidcylinder }}\,>\,a_{\text {solidsphere }}$

$\Rightarrow v_{\text {ring }}\,<\,v_{\text {solid cylinder }}\,<\,v_{\text {solid sphere }}$

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