Question

if the volume of earth become eight time the present value with keeping its mass constant the new value of gravitational acceleration at the surface of earth will be​

Answer 1

Answer:

9.8 metreper second square

Answer 2

Answer:

$\frac{g}{4}$

Explanation:

Let initially mass of earth=M

Initial volume of earth=v

According to question

V=8v

Mass=Constant

We have to find the gravitational acceleration at the surface of earth.

Initial gravitational acceleration=$\frac{GM}{r^2}$

Volume of sphere=$\frac{4}{3}\pi r^3$

Initial volume of earth=$\frac{4}{3}\pi r^3$

New volume of earth=V=$\frac{4}{3}\pi r'^3$

$8\times \frac{4}{3}\pi r^3=\frac{4}{3}\pi r'^3$

$r'=2r$

New radius of earth=r'=2r

New gravitational acceleration=$g'=\frac{GM}{(2r)^2}=\frac{1}{4}\cdot \frac{GM}{r^2}=\frac{g}{4}$

Hence, the new acceleration at the surface of earth will be =$\frac{g}{4}$