If the radius of the earth were to shrink by | vedclass

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

Question

(C) The acceleration due to gravity $g$ on the surface of the earth is given by $g = \frac{GM}{R^2}$,where $G$ is the gravitational constant,$M$ is th

Vedclass · Accepted Answer

Increase by $2\%$

Vedclass · Answer

(C) The acceleration due to gravity $g$ on the surface of the earth is given by $g = \frac{GM}{R^2}$,where $G$ is the gravitational constant,$M$ is the mass of the earth,and $R$ is the radius of the earth.Taking the natural logarithm on both sides,we get $\ln g = \ln G + \ln M - 2 \ln R$.Differentiating both sides,we get the relative error formula: $\frac{\Delta g}{g} = -2 \left( \frac{\Delta R}{R} ight)$.Given that the radius shrinks by $1\%$,we have $\frac{\Delta R}{R} = -0.01$.Substituting this value,we get $\frac{\Delta g}{g} = -2 	imes (-0.01) = 0.02$.This represents an increase of $2\%$ in the acceleration due to gravity.

If the radius of the earth were to shrink by $1\%$ and its mass remained the same,the acceleration due to gravity on the earth's surface would

Similar Questions

An $\alpha$-particle of energy $E$ is liberated during the decay of a nucleus of mass number $236$. The total energy released in this process is

Which of the following absorbs light energy during photosynthesis?

The product $\begin{array}{*{20}{c}} {CH_2 - O - COCH_3} \\ {|} \\ {CH_2 - O - COCH_3} \end{array}$ is obtained by the reaction of which of the following?

Which domain of life is known for surviving in extreme environmental conditions?

Vedclass Test Series

Exam Paper Generator

Online Exam Module