For a sphere of mass M and radius R,if the gr | vedclass

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

Question

(A) The gravitational force $F$ on a test mass $m$ is given by $F = mI$,where $I$ is the gravitational field intensity.Case $1$: For points outside th

Vedclass · Accepted Answer

$\frac{F_1}{F_2} = \frac{r_1}{r_2}$ if $r_1 < R$ and $r_2 < R$

Vedclass · Answer

(A) The gravitational force $F$ on a test mass $m$ is given by $F = mI$,where $I$ is the gravitational field intensity.Case $1$: For points outside the sphere $(r > R)$:The gravitational field intensity is $I = \frac{GM}{r^2}$.Thus,$F \propto \frac{1}{r^2}$.Therefore,$\frac{F_1}{F_2} = \frac{r_2^2}{r_1^2}$ for $r_1 > R$ and $r_2 > R$.Case $2$: For points inside the sphere $(r The gravitational field intensity is $I = \frac{GMr}{R^3}$.Thus,$F \propto r$.Therefore,$\frac{F_1}{F_2} = \frac{r_1}{r_2}$ for $r_1 Comparing these with the given options,option $A$ is correct.

For a sphere of mass $M$ and radius $R$,if the gravitational forces at distances $r_1$ and $r_2$ from the center are $F_1$ and $F_2$ respectively,then:

Similar Questions

Assuming the Earth to be a sphere of uniform mass density,how much would a body weigh (in $N$) halfway down to the centre of the Earth if it weighed $250 \; N$ on the surface?

The height in terms of radius of the earth $(R)$, at which the acceleration due to gravity becomes $g/9$, where $g$ is acceleration due to gravity on earth's surface, is . . . . . . .

Considering Earth to be a sphere of radius $R$ having uniform density $\rho$,the value of acceleration due to gravity $g$ in terms of $R$,$\rho$,and $G$ is:

The rotation of the Earth (of radius $R$) about its axis speeds up to a value such that a man at latitude angle $45^{\circ}$ feels weightlessness. The duration of a day in such a case is

What should be the angular speed with which the Earth must rotate on its axis so that a person on the equator would weigh $\frac{3}{5}$ th as much as their present weight?

Vedclass Test Series

Exam Paper Generator

Online Exam Module