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# A ring has a total mass M but not uniformly distributed over its circumference . The radius of ring is R. A Point mass m is placed at the center of the ring. Work done in taking away this point mass from center to infinity is

$(a)\;\frac{-GMm}{R} \quad (b)\;\frac{GMm}{R} \quad (c)\;\frac{GMm}{2R} \quad (d)\;can\;not\;be\;calculated$

Can you answer this question?

Work done=increase in potential energy of system
$\qquad=V_f-V_i$
$\qquad=m(V_f-V_i)\qquad V-$ gravitational potential
Even if mass is not distributed uniformly potential at center is $\large\frac{-GM}{R}$
$W= m \bigg[ 0-\bigg(\large\frac{-GM}{R}\bigg)\bigg]$
$\qquad= \large\frac{GMm}{R}$
Hence b is the correct answer.

answered Aug 21, 2013 by
edited Feb 17, 2014 by meena.p