Question

A solid sphere is in a rolling motion. In rolling motion, a body possesses translational kinetic energy (k_t) as well as rotational kinetic energy (k_r) simultaneously. The ratio k_t : k_r for the sphere is:

Options

• 10 : 7

• 5 : 7

• 2 : 5

• 5 : 2

Answer 1

5 : 2

Explanation:

Kinetic energy translational (k_t) = `1/2 "mv"^2`

Kinetic energy rotational, (k_r) = `1/2 "I" ω^2`

= `1/2 (2/5 "mr"^2) xx "v"^2/"r"^2 = 2/10 "mv"^2`

∴ `"k"_"t"/"k"_"r" = 5/2`