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  • A body of mass m is approaching towards the centre of a hypothetical hollow planet of mass M and radius R. The speed of the body when it passes the centre of the planet through its diametrical chut

A body of mass m is approaching towards the centre of a hypothetical hollow planet of mass M and radius R. The speed of the body when it passes the centre of the planet through its diametrical chute is

Option: 1

\mathrm{\sqrt{\frac{G M}{R}}}


Option: 2

\mathrm{\sqrt{\frac{2G M}{R}}}


Option: 3

Zero


Option: 4

none of these.


Answers (1)

best_answer

At infinity, the total energy of the body is zero. Therefore the total energy of the body just before hitting the planet P will be zero according to the conservation of energy

\mathrm{\begin{aligned} & \Rightarrow \mathrm{F}_{\mathrm{p}}=\mathrm{E}_{\infty}=0 \quad \Rightarrow \quad \mathrm{U}_{\mathrm{p}}+\mathrm{K}_{\mathrm{p}}=0 \\ & \Rightarrow-\frac{\mathrm{GMm}}{\mathrm{R}}+\frac{1}{2} \mathrm{mv}^2=0 \\ & \Rightarrow \mathrm{v}=\sqrt{\frac{2 \mathrm{GM}}{\mathrm{R}}} . \end{aligned}}

Since the force imparted on a particle inside spherical shell is zero, therefore the velocity of the particle inside the spherical shell remain constant. Therefore, the body passes the centre of the planet with same speed \mathrm{v=\sqrt{\frac{2 \mathrm{GM}}{\mathrm{R}}}} .

Therefore (B).

Posted by

Rishabh

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