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  4. 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 H < < R above the earth’s surface, and reaches the earth’s surface in time t. Then t is equal to

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Q. 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 $H < < R$ above the earth’s surface, and reaches the earth’s surface in time $t$. Then $t$ is equal to

Gravitation

Solution:

As the masses of the body and the earth are comparable, they will move towards their centre of mass, which remains stationary
image
Hence the body of mass $2m$ move through distance $\frac{H}{3}$.
and time to reach the earth surface
$=\sqrt{\frac{2h}{g}} = \sqrt{\frac{2H/3}{g}} $
$= \sqrt{\frac{2H}{3g}}$