Assume that a tunnel is dug through the Earth | vedclass

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

Question

(B) When a particle of mass $m$ is at a distance $r$ from the center of the Earth,the gravitational force acting on it is due only to the mass of the

Vedclass · Accepted Answer

$\left( \frac{4\pi}{3} mG\rho \right) r$

Vedclass · Answer

(B) When a particle of mass $m$ is at a distance $r$ from the center of the Earth,the gravitational force acting on it is due only to the mass of the Earth contained within a sphere of radius $r$. Let this mass be $M'$.The volume of this inner sphere is $V' = \frac{4}{3} \pi r^3$.Since the density $\rho$ is uniform,the mass $M'$ is given by $M' = \rho V' = \rho \left( \frac{4}{3} \pi r^3 \right)$.The gravitational force $F$ on the particle of mass $m$ at distance $r$ is given by Newton's law of gravitation:$F = \frac{G M' m}{r^2}$Substituting the value of $M'$:$F = \frac{G m}{r^2} \left( \rho \cdot \frac{4}{3} \pi r^3 \right)$Simplifying the expression:$F = \left( \frac{4}{3} \pi G \rho \right) m r$

Assume that a tunnel is dug through the Earth from the North Pole to the South Pole and that the Earth is a non-rotating,uniform sphere of density $\rho$. The gravitational force on a particle of mass $m$ dropped into the tunnel when it reaches a distance $r$ from the center of the Earth is:

Similar Questions

The height $h$ at which the weight of a body will be the same as that at the same depth $h$ from the surface of the earth is (Radius of the earth is $R$ and effect of the rotation of the earth is neglected):

The radii of two planets $A$ and $B$ are $R$ and $4R$ and their densities are $\rho$ and $\rho/3$ respectively. The ratio of acceleration due to gravity at their surfaces $(g_A : g_B)$ will be

$A$ body has a weight of $90 \ kgf$ on the earth's surface. The mass of the moon is $1/9$ of the earth's mass and its radius is $1/2$ of the earth's radius. On the moon,the weight of the body is .......... $kgf$.

If the density of the earth is doubled keeping its radius constant,then the acceleration due to gravity will be........ $m/s^2$. $(g = 9.8\,m/s^2)$

If a man at the equator would weigh $(3/5)^{th}$ of his weight,the angular speed of the earth is

Vedclass Test Series

Exam Paper Generator

Online Exam Module