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Question: A small body of superdense material, whose mass is twice the mass of the earth but whose size is ver...

A small body of superdense material, whose mass is twice the mass of the earth but whose size is very small compared to the size of the earth, starts from rest at a height above the earth’s surface, and reaches the earth’s surface in time t. Then t is equal to

A

2H/g\sqrt { 2 H / g }

B

H/g\sqrt { H / g }

C

2H/3g\sqrt { 2 H / 3 g }

D

4H/3g\sqrt { 4 H / 3 g }

Answer

2H/3g\sqrt { 2 H / 3 g }

Explanation

Solution

As the masses of the body and the earth are comparable, they will move towards their centre of mass, which remains stationary.

Hence the body of mass 2m move through distance H3\frac { H } { 3 }.

and time to reach the earth surface =2hg= \sqrt { \frac { 2 h } { g } } =2H/3g= \sqrt { \frac { 2 H / 3 } { g } }

=2H3g= \sqrt { \frac { 2 H } { 3 g } }