What is the depth at which the value of accel | vedclass

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

Question

(C) The value of acceleration due to gravity at a depth $d$ below the surface of the Earth is given by the formula:$g' = g \left(1 - \frac{d}{R}\right

Vedclass · Accepted Answer

$\frac{R(n-1)}{n}$

Vedclass · Answer

(C) The value of acceleration due to gravity at a depth $d$ below the surface of the Earth is given by the formula:$g' = g \left(1 - \frac{d}{R}\right)$where $g$ is the acceleration due to gravity at the surface and $R$ is the radius of the Earth.According to the problem,the value of acceleration at depth $d$ is $\frac{1}{n}$ times the value at the surface:$g' = \frac{g}{n}$Substituting this into the formula:$\frac{g}{n} = g \left(1 - \frac{d}{R}\right)$Dividing both sides by $g$:$\frac{1}{n} = 1 - \frac{d}{R}$Rearranging the terms to solve for $d$:$\frac{d}{R} = 1 - \frac{1}{n}$$\frac{d}{R} = \frac{n-1}{n}$$d = R \left(\frac{n-1}{n}\right)$

What is the depth at which the value of acceleration due to gravity becomes $\frac{1}{n}$ times the value at the surface of the Earth? (radius of Earth $= R$)

Similar Questions

At a height of $10 \,km$ above the surface of the earth,the value of acceleration due to gravity is the same as that at a particular depth below the surface of the earth. Assuming uniform mass density for the earth,the depth is ............. $km$.

$A$ spherical part of radius $R/2$ is excavated from an asteroid of mass $M$ and radius $R$ as shown in the figure. The gravitational acceleration at a point on the surface of the asteroid just above the excavation is

The depth $d$ at which the value of acceleration due to gravity becomes $\left(\frac{1}{n}\right)$ times the value at the surface of the earth is ($R=$ radius of the earth).

Since the Earth is not a perfect sphere,what is the effect on the acceleration due to gravity $(g)$?

When a ball is dropped from a height $h$,it takes $t \ s$ to reach the ground. If the same experiment is done on a different planet having a mass $100$ times the earth's mass and a radius $10$ times the earth's radius,then the time it will take to cover the same height on the new planet is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module