Question

A chain of length `l = pi R//4` is placed. On a smooth hemispherical surface of radius `R` with one of its ends fixed at the top of the sphere. Mass of chain is `sqrt(pi kg)` and `R = 1m.(g = 10 m//s^(2))`.
The gravitational potential energy of the chain considering reference level at the base of hemisphere is
A. 20 J
B. `20 sqrt(2) J`
C. 40 J
D. `40 sqrt(2) J`

Answer 1

Correct Answer - C
`dm =(m)/(l) Rd theta, PE = underset(0) overset(pi 4) int (M)/(l) Rd thetagR cos theta`
=`(M)/(l) gR^(2) sin 45^@ = 40 J`.