A particle of mass m is dropped from a height | vedclass

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(D) The correct option is $(d)$.$1$. When the particle is outside the earth (at a distance $r > R$ from the center),the gravitational force acting on

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Both $(a)$ and $(b)$

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(D) The correct option is $(d)$.$1$. When the particle is outside the earth (at a distance $r > R$ from the center),the gravitational force acting on it is $F = \frac{GMm}{r^2}$,which is proportional to $\frac{1}{r^2}$.$2$. When the particle is inside the tunnel (at a distance $r $3$. In both regions,the force is always directed towards the center of the earth. Since the particle is dropped from a height $R$ above the surface,it will fall into the tunnel,pass through the center,and reach a height $R$ on the other side due to the conservation of mechanical energy.$4$. The motion is repetitive and bounded,making it periodic and oscillatory. However,because the force is not proportional to the displacement from the equilibrium position throughout the entire path (it changes from $\propto \frac{1}{r^2}$ to $\propto r$),the motion is not simple harmonic $(SHM)$.Therefore,both statements $(a)$ and $(b)$ are correct.

Column $-I$	Column $-II$
$(A)$ Kinetic energy	$(p)$ $-\frac{GM_Em}{2r}$
$(B)$ Potential energy	$(q)$ $\sqrt{\frac{GM_E}{r}}$
$(C)$ Total energy	$(r)$ $-\frac{GM_Em}{r}$
$(D)$ Orbital velocity	$(s)$ $\frac{GM_Em}{2r}$

$A$ particle of mass $m$ is dropped from a height $R$ equal to the radius of the earth above the tunnel dug through the earth as shown in the figure. Hence the correct statement is

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