Question

In an experiment, Ram is being provided a frictionless inclined track that ends in a circular loop of diameter D. Ram put a body on this track and allows it to slide down this track under gravity from a height of 10 cm. The body is just able to complete the circular track. Whats the diameter of the track?

Answer 1

The diameter of the circular track should be 8 cm.

Explanation :

At the top of the track, potential energy

PE = mgh

At the bottom of the track, kinetic energy

KE = mv²/2

according to conservation of energy, KE = PE

=> mv²/2 = mgh

=> v = √2gh

we know that to complete a vertical circular track the body should have a velocity at the bottom as :

v = √5rg

hence,

√2gh = √5rg

=> r = 2h/5

=> r = 2 x 10/5 = 4

=> D = 2r = 8 cm

Hence the diameter of the circular track should be 8 cm.