State whether the following statement is True or False:
The value of $g$ is zero at the centre of the earth.
The value of $g$ is zero at the centre of the earth.
(TRUE) The statement is True.
According to the formula for acceleration due to gravity at a depth $d$ below the surface of the Earth,$g_d = g(1 - d/R)$,where $g$ is the acceleration due to gravity at the surface,$d$ is the depth,and $R$ is the radius of the Earth.
At the centre of the Earth,the depth $d$ is equal to the radius $R$ $(d = R)$.
Substituting $d = R$ into the formula,we get $g_d = g(1 - R/R) = g(1 - 1) = g(0) = 0$.
Therefore,the acceleration due to gravity $(g)$ at the centre of the Earth is zero.
According to the formula for acceleration due to gravity at a depth $d$ below the surface of the Earth,$g_d = g(1 - d/R)$,where $g$ is the acceleration due to gravity at the surface,$d$ is the depth,and $R$ is the radius of the Earth.
At the centre of the Earth,the depth $d$ is equal to the radius $R$ $(d = R)$.
Substituting $d = R$ into the formula,we get $g_d = g(1 - R/R) = g(1 - 1) = g(0) = 0$.
Therefore,the acceleration due to gravity $(g)$ at the centre of the Earth is zero.
Explore More
Similar Questions
If your weight on the Earth is $450 N$,calculate your weight on planet Mars. (Radius of Mars $= 4.3 \times 10^{6} m$,mass of Mars $= 6 \times 10^{23} kg$ and gravitational constant $G = 6.67 \times 10^{-11} Nm^{2} kg^{-2}$). Take acceleration due to gravity on Earth as $10 m s^{-2}$.
Medium
View Solution$(a)$ What do you mean by free fall?
$(b)$ What happens to the direction of motion of objects during free fall?
$(c)$ $A$ stone is dropped from a height of $19.6 \, m$. Calculate:
$(i)$ Time taken to fall.
$(ii)$ How fast does it move at the end of this fall?
$(iii)$ Acceleration after $1 \, s$.
$(b)$ What happens to the direction of motion of objects during free fall?
$(c)$ $A$ stone is dropped from a height of $19.6 \, m$. Calculate:
$(i)$ Time taken to fall.
$(ii)$ How fast does it move at the end of this fall?
$(iii)$ Acceleration after $1 \, s$.
Medium
View SolutionThe value of the gravitational constant $(G)$ depends upon:
Easy
View Solution$A$ stone is released from the top of a tower of height $19.6 \, m$. Calculate its velocity just before touching the ground.
Easy
View Solution$A$ ball is thrown vertically upwards with a velocity $u$. Calculate the velocity with which it falls to the earth again.
Medium
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo