If both the mass and the radius of the earth | vedclass

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

Question

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

Vedclass · Accepted Answer

increase by $1\%$

Vedclass · Answer

(B) The acceleration due to gravity $g$ 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.Taking the logarithmic differentiation of the expression,we get: $\frac{dg}{g} = \frac{dM}{M} - 2 \frac{dR}{R}$.Given that both mass $M$ and radius $R$ decrease by $1\%$,we have $\frac{dM}{M} = -1\%$ and $\frac{dR}{R} = -1\%$.Substituting these values into the equation: $\frac{dg}{g} 	imes 100\% = (-1\%) - 2(-1\%) = -1\% + 2\% = +1\%$.Therefore,the value of the acceleration due to gravity will increase by $1\%$.

If both the mass and the radius of the earth decrease by $1\%$,the value of the acceleration due to gravity will

Similar Questions

Consider a metal sphere of radius $R$ that is cut in two parts along a plane whose minimum distance from the sphere's centre is $h$. The sphere is uniformly charged by a total electric charge $Q$. The minimum force necessary to hold the two parts of the sphere together is:

Charge $q$ is uniformly distributed over a thin half ring of radius $R$. The electric field at the centre of the ring is

$\int \tan ^{-1}\left(\sqrt{\frac{1-x}{1+x}}\right) d x$ is equal to

Which of the following cylindrical rods will conduct the most heat when their ends are maintained at the same steady temperatures?

Phloem loading is related to:

Vedclass Test Series

Exam Paper Generator

Online Exam Module