A uniform solid sphere of radius R produces a | vedclass

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

Question

(C) The gravitational acceleration $g$ at a distance $r$ from the centre of a uniform solid sphere of mass $M$ and radius $R$ (where $r \ge R$) is giv

Vedclass · Accepted Answer

$2 R$

Vedclass · Answer

(C) The gravitational acceleration $g$ at a distance $r$ from the centre of a uniform solid sphere of mass $M$ and radius $R$ (where $r \ge R$) is given by $g = \frac{GM}{r^2}$.On the surface,$r = R$,so $a_o = \frac{GM}{R^2}$.We want to find the distance $r$ where the acceleration becomes $a = \frac{a_o}{4}$.Substituting the expressions,we get $\frac{GM}{r^2} = \frac{1}{4} \left( \frac{GM}{R^2} \right)$.Canceling $GM$ from both sides,we get $\frac{1}{r^2} = \frac{1}{4R^2}$.Taking the square root of both sides,$r^2 = 4R^2$,which gives $r = 2R$.Thus,the distance from the centre of the sphere is $2R$.

$A$ uniform solid sphere of radius $R$ produces a gravitational acceleration of $a_o$ on its surface. The distance of the point from the centre of the sphere where the gravitational acceleration becomes $\frac{a_o}{4}$ is,

Similar Questions

At what altitude will the acceleration due to gravity be $25\%$ of that at the earth's surface (given radius of earth is $R$)?

The weight of a body of mass $m$ decreases by $1\%$ when it is raised to a height $h$ above the Earth's surface. If the body is taken to a depth $h$ in a mine,the change in its weight is:

Find the gravitational field at a distance of $2000\, km$ from the center of the Earth. (in $m/s^2$)
(Given: $R_{\text{earth}} = 6400\, km$,$r = 2000\, km$,$M_{\text{earth}} = 6 \times 10^{24}\, kg$)

The height $h$ above the earth's surface at which the value of acceleration due to gravity $g$ becomes $\frac{g}{3}$ is ($R=$ radius of the earth).

$g_e$ and $g_p$ denote the acceleration due to gravity on the surface of the Earth and another planet whose mass and radius are twice that of the Earth. Then:

Vedclass Test Series

Exam Paper Generator

Online Exam Module