Question

A system consists of n identical particles of mass m placed rigidly on the vertices of a regular polygon with each side of length l if k isthe k.E imparted to one of the particles so that it just escape the gravitational pull of the system and thereafter k.E k2 is given to the adjecent particle to escape then the difference k1 -k2 is

Answer 1

K1 - K2 = Gm2/a

Explanation:

Let potential due to (n-1) particles at location of first mass = -V

Potential energy of mass m = -Vm

V*m = K1 ----------------(1)

Potential at lcoatin of its neighbour will be V1 = -V - (-Gm/a) = Gm/a - V

Potential energy of adjacent particle will be V2 = mV1 = m ( - V + Gm/a)

V2 + K2 = 0

K2 = m (V - Gm/a) = mV - Gm2/a -------- (2)

K1 - K2 = Vm - (Vm -  Gm2/a ) = Gm2/a