A solid cylinder and a hollow cylinder, both of the same mass and… - Vidyadip

MCQ

A solid cylinder and a hollow cylinder, both of the same mass and same external diameter are released from the same height at the same time on a inclined plane. Both roll down without slipping. Which one will reach the bottom first?

✓
Solid cylinder
B
Hollow cylinder
C
Both together
D
Both together only when angle of inclination of plane is $45^o$

✓

Answer

Correct option: A.

Solid cylinder

a
Time taken to reach the bottom of inclined plane.

$\sqrt{\frac{2 l\left(1+\frac{K^{2}}{R^{2}}\right)}{g \sin \theta}}$

Here, / is length of incline plane

For solid cylinder $K^{2}=\frac{R^{2}}{2}$

For hollow cylinder $K^{2}=R^{2}$

Hence, solid cylinder will reach the bottom first.

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