Question

If the volume of Earth becomes 8 times the present value with keeping it's mass constant,the new value of gravitational acceleration at surface of Earth will be.




a) g/8
b) g/4
c) 2g
d)2

Answer 1

Answer:

g/4. is answer for this question

Answer 2

The new gravitational acceleration is $\dfrac{g}{4}$

(b) is correct option.

Explanation:

Given that,

The volume of Earth becomes 8 times the present value with keeping it's mass constant,

$V' = 8V$

Let initial mass of earth is M.

Initial volume = V

Volume of surface $V= \dfrav{4}{3}\pir^3$

Initial volume of earth $V=\dfrav{4}{3}\pir^3$

New volume of earth $V= \dfrav{4}{3}\pir'^3$

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

$8r^3=r'^3$

$r'=2r$

New radius of earth r'=2r

We need to calculate the new gravitational acceleration

$g'=\dfrac{GM}{(2r)^2}$

$g'=\dfrac{1}{4}g$

Hence, The new gravitational acceleration is $\dfrac{g}{4}$

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Topic : gravitational acceleration

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