AP EAMCET201823 Apr 2018Evening ShiftPhysicsWork, Power and EnergyActual
A uniform chain of length l and mass m lies on the surface of a smooth hemisphere of radius R(R>l) with one end tied to the top the hemisphere as shown in the figure. Gravitational potential energy of the chain with respect to the base of the hemisphere is
Options
- Am g l 2
- Bm g R^2 l ( I R )
- Cm g R^2 l ( R l )
- Dm g l^2 R ( l R )
Correct answer
B. m g R^2 l ( I R )
Step-by-step solution
We have, h R = or h=R Also, d l=R d Mass of d l length of chain =d m= m l d l PE of d m mass =d U=d m g h= m g h l d l= m g h l R d = m g R^2 l d So, PE of complete chain is U= _ / 2 ^ / 2- d U= m g R^2 l ( l R )