If a hole is bored along the diameter of the | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) When a stone is dropped into a hole bored along the diameter of the earth,the gravitational force acting on the stone at a distance $r$ from the c

Vedclass · Accepted Answer

The stone executes simple harmonic motion about the centre of the earth.

Vedclass · Answer

(C) When a stone is dropped into a hole bored along the diameter of the earth,the gravitational force acting on the stone at a distance $r$ from the centre is given by $F = -(\frac{GMm}{R^3})r$. Since the force is proportional to the displacement $r$ and directed towards the centre,the stone undergoes simple harmonic motion ($S$.$H$.$M$.) about the centre of the earth. The time period of this oscillation is given by $T = 2\pi \sqrt{\frac{R}{g}}$,where $R$ is the radius of the earth and $g$ is the acceleration due to gravity at the surface.

If a hole is bored along the diameter of the earth and a stone is dropped into the hole,what happens to the stone?

Similar Questions

$A$ spherical planet far out in space has a mass $M_0$ and diameter $D_0$. $A$ particle of mass $m$ falling freely near the surface of this planet will experience an acceleration due to gravity which is equal to

If the radius of the earth were to shrink by $1\%$ while its mass remains the same,the acceleration due to gravity on the earth's surface would

$A$ body weighs $72 \ N$ on the surface of the earth. What is the gravitational force on it at a height equal to half the radius of the earth (in $N$)?

The rotation of the earth having radius $R$ about its axis speeds up to a value such that a man at latitude angle $60^{\circ}$ feels weightless. The duration of the day in such case will be:

Vedclass Test Series

Exam Paper Generator

Online Exam Module