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 an inclined plane. Both roll down without slipping. Which one will reach the bottom first?

Question

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 an inclined plane. Both roll down without slipping. Which one will reach the bottom first? (A) Both together only when angle of inclination of plane is 45° (B) Both together (C) Hollow cylinder (D) Solid cylinder

Tardigrade Admin · Accepted Answer

Time taken to reach the bottom of inclined plane.

t = \frac{2 l ( 1 + \frac{K ^{2}}{R ^{2}} )}{g s i n θ}

Here,

l

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.

Q. 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 an inclined plane. Both roll down without slipping.
Which one will reach the bottom first?

Both together only when angle of inclination of plane is $4 5^{\circ}$

Both together

Hollow cylinder

Solid cylinder

Time taken to reach the bottom of inclined plane.
$t = \frac{2 l ( 1 + \frac{K ^{2}}{R ^{2}} )}{g s i n θ}$
Here, $l$ 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.

Q. 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 an inclined plane. Both roll down without slipping. Which one will reach the bottom first?

Both together only when angle of inclination of plane is 45∘