If the radius of the Earth shrinks by 1.5 % ( | vedclass

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

Question

(C) The gravitational acceleration $g$ is given by the formula $g = \frac{GM}{R^2}$,where $G$ is the gravitational constant,$M$ is the mass of the Ear

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(C) The gravitational acceleration $g$ is given by the formula $g = \frac{GM}{R^2}$,where $G$ is the gravitational constant,$M$ is the mass of the Earth,and $R$ is its radius.Since the mass $M$ remains constant,we have $g \propto \frac{1}{R^2}$.Taking the logarithmic derivative,we get $\frac{\Delta g}{g} = -2 \frac{\Delta R}{R}$.Given that the radius shrinks by $1.5 \%$,we have $\frac{\Delta R}{R} = -1.5 \% = -0.015$.Substituting this value into the equation:$\frac{\Delta g}{g} = -2 	imes (-1.5 \%) = +3 \%$.Therefore,the gravitational acceleration increases by $3 \%$.

If the radius of the Earth shrinks by $1.5 \%$ (mass remaining same),then the value of gravitational acceleration changes by ......... $\%$

Similar Questions

$Assertion$ : In a free fall,weight of a body becomes effectively zero.
$Reason$ : Acceleration due to gravity acting on a body having free fall is zero.

The height of the point vertically above the earth's surface,at which the acceleration due to gravity becomes $1\%$ of its value at the surface is (Radius of the earth $= R$). (in $,R$)

Obtain the general equation of gravitational force at a distance $r$ from the centre of the Earth and derive the equation for acceleration due to gravity on the surface of the Earth.

The mass of the earth is $81$ times that of the moon and the radius of the earth is $3.5$ times that of the moon. The ratio of the acceleration due to gravity at the surface of the moon to that at the surface of the earth is

In order to make the effective acceleration due to gravity equal to zero at the equator,the angular velocity of rotation of the earth about its axis should be $(g = 10\,m/s^2$ and radius of earth is $6400\,km)$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module