Question

A small body slides down a smooth uneven surface from a height H which eventually emerges into a circular loop of radius R(

Answer 1

Given,

A frictionless track ABCDE ends in a circular loop of radius R. A body slides down the track from point A which is at height h = 5cm. Maximum value of R for a body to complete the loop.

To complete the circle,

minimum velocity require at the bottom of circle (at point B), v = √5gR ......(1)

velocity of small body when it reaches at point B from A is v.

from conservation of work energy theorem,

kinetic energy = workdone by body

⇒1/2 mv² = mg × h

⇒v² = 2gh

from equation (1),

⇒5gR = 2gh

⇒R = 2h/5 = 2 × 5cm/5 = 2cm

Therefore radius of the circular loop is 2cm.