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

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

Question

(B) The gravitational force on a particle of mass $m$ at a distance $r$ from the center of the Earth (where $r < R_e$) is given by $F = -\frac{GMmr}{R

Vedclass · Accepted Answer

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

Vedclass · Answer

(B) The gravitational force on a particle of mass $m$ at a distance $r$ from the center of the Earth (where $r Since $F \propto -r$,the force is a restoring force proportional to the displacement from the center,which is the condition for Simple Harmonic Motion $(SHM)$. Thus,Assertion $(A)$ is true.The Reason $(R)$ states Newton's Law of Gravitation,which is also a true statement $(F \propto 1/r^2)$.However,the motion inside the Earth is governed by the effective gravitational field inside a sphere,where the force is proportional to $r$,not $1/r^2$. Therefore,$(R)$ is not the correct explanation for $(A)$.

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

Similar Questions

Derive the equation for the variation of $g$ due to height from the surface of the Earth.

Two planets of radii in the ratio $2 : 3$ are made from the material of density in the ratio $3 : 2$. Then the ratio of acceleration due to gravity $g_1/g_2$ at the surface of the two planets will be

The dependence of acceleration due to gravity $g$ on the distance $r$ from the centre of the earth,assumed to be a sphere of radius $R$ of uniform density,is as shown in the figure below. The correct figure is:

The weights of an object are measured in a coal mine of depth $h_1$,then at sea level of height $h_2=0$,and lastly at the top of a mountain of height $h_3$ as $W_1, W_2$,and $W_3$ respectively. Which one of the following relations is correct? [$h_1 \ll R, h_3 \ll R, R=$ radius of the earth]

Where will it be profitable to purchase $1$ kilogram of sugar?

Vedclass Test Series

Exam Paper Generator

Online Exam Module

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