From a sphere of mass M and radius R,a smalle | vedclass

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

Question

(A) Let the density of the sphere be $ho$.Mass of the original sphere $M = ho \cdot \frac{4}{3}\pi R^3$.Volume of the removed sphere $V_{	ext{rem

Vedclass · Accepted Answer

$\frac{7GM^2}{576R^2}$

Vedclass · Answer

(A) Let the density of the sphere be $ho$.Mass of the original sphere $M = ho \cdot \frac{4}{3}\pi R^3$.Volume of the removed sphere $V_{	ext{removed}} = \frac{4}{3}\pi (\frac{R}{2})^3 = \frac{1}{8} (\frac{4}{3}\pi R^3)$.Mass of the removed sphere $m = ho \cdot V_{	ext{removed}} = \frac{M}{8}$.Mass of the remaining part of the sphere $M' = M - m = M - \frac{M}{8} = \frac{7M}{8}$.The gravitational force between the remaining part of the sphere and the removed sphere is given by Newton's law of gravitation:$F = \frac{G M' m}{r^2}$Here,$r = 3R$ is the distance between the centers of the two spheres.$F = \frac{G (\frac{7M}{8}) (\frac{M}{8})}{(3R)^2}$$F = \frac{G (\frac{7M^2}{64})}{9R^2}$$F = \frac{7GM^2}{576R^2}$

From a sphere of mass $M$ and radius $R$,a smaller sphere of radius $\frac{R}{2}$ is carved out. For the configuration shown in the figure where the distance between the center of the original sphere and the center of the removed sphere is $3R$,the gravitational force between the two spheres is:

Similar Questions

Two spheres of radius $R$ are placed in contact as shown in the figure. If the mass density of each sphere is $\rho$,find the gravitational force between them.

Consider an infinite distribution of point masses (each of mass $m$) placed on the $x$-axis as shown in the diagram. What is the gravitational force acting on the point mass placed at the origin?

Two spheres of mass $m$ and $M$ are situated in air and the gravitational force between them is $F$. The space around the masses is now filled with a liquid of specific gravity $3$. The gravitational force will now be

Let $G, W, E$ and $S$ be the relative strengths of gravitational, weak-nuclear, electromagnetic, and strong-nuclear forces, respectively. Which of the following statements is correct?

Two particles of mass $m_{1}$ and $m_{2}$ approach each other due to their mutual gravitational attraction only. Then,

Vedclass Test Series

Exam Paper Generator

Online Exam Module