Derive an expression for the speed of a body of mass that starts from rest at a…

PHYSICS · Subjective · CBSE · Physics · Gravitation · Gravitation

Problem

Derive an expression for the speed

v

of a body of mass

m

that starts from rest at a distance

r_{1}

from the centre of a planet of mass

M

and moves radially inward to a distance

r_{2}

(r_{2}<r_{1})

. Show that

v = \sqrt{\,2GM\!\left(\frac{1}{r_{2}}-\frac{1}{r_{1}}\right)}.