Assertion (A): A particle of mass m dropped i | vedclass

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(B) For a particle of mass $m$ inside the Earth at a distance $r$ from the center,the gravitational force is given by $F = -\frac{GMmr}{R^3}$,where $M

Vedclass · Accepted Answer

Both $(A)$ and $(R)$ are true but $(R)$ is not the correct explanation of $(A)$

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(B) For a particle of mass $m$ inside the Earth at a distance $r$ from the center,the gravitational force is given by $F = -\frac{GMmr}{R^3}$,where $M$ is the mass of the Earth and $R$ is its radius.This force is proportional to the displacement $r$ and directed towards the center,which is the condition for simple harmonic motion $(SHM)$. Thus,Assertion $(A)$ is true.The Reason $(R)$ states that the gravitational force is inversely proportional to the square of the distance $(F \propto 1/r^2)$. This is Newton's Law of Gravitation,which is true for particles outside the Earth or at the surface. However,inside the Earth,the effective force depends on the mass enclosed within the sphere of radius $r$,leading to a linear dependence on $r$.While $(R)$ is a true statement about universal gravitation,it does not explain why the motion inside the Earth is simple harmonic (which depends on the linear force law inside the Earth). Therefore,$(R)$ is not the correct explanation of $(A)$.

Assertion $(A)$: $A$ particle of mass $m$ dropped into a hole made along the diameter of the Earth from one end to the other executes simple harmonic motion.
Reason $(R)$: Gravitational force between any two particles is inversely proportional to the square of the distance between them.

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Assertion $(A)$: $A$ particle of mass $m$ dropped into a hole made along the diameter of the Earth from one end to the other executes simple harmonic motion.Reason $(R)$: Gravitational force between any two particles is inversely proportional to the square of the distance between them.