Question

A frictionless track 12345 ends in a circular loop of radius R. A body slides down the track from point 1 Which is 6 cm. Maximum value of R for the body to successfully complete the loop is 

(A) 6 cm 

(B) (15 / 4) cm

(C) (5 / 12) cm 

(D) (12 / 5) cm

Answer 1

Correct option: (D) (12 / 5) cm

Explanation:

let speed at bottom = V_B 

The minimum velocity at the bottom of a body to complete vertical circle is √5gR

hence V_B = √5gR

P.E of body = KE in motion

mgh = (1/2)mV² 

gh = {(V_B²) / 2}

V_B = √2gh

 hence

√5gR = √2gh

R = (2/5)h

R = (2/5) × 6

R = (12 / 5) cm