Question

derive how does the value of gravitational force f between two objects change when (a) distance between them is reduced to half and (b)mass of an object is increased four times​

Answer 1

Answer:

Explanation:

Given below.Hope it helps..

Answer 2

(A) New force becomes 4 times of the initial force.

(B) New force becomes 4 times of the initial force.

Explanation:

The gravitational force between two masses is given by the formula as :

$F=G\dfrac{m_1m_2}{r^2}$

r is the distance between masses

(a) If the distance between them is reduced to half, d' = d/2

New force,

$F'=G\dfrac{m_1m_2}{(d/2)^2}\\\\F'=4G\dfrac{m_1m_2}{(d)^2}\\\\F'=4\times F$

New force will becomes 4 times of the initial force.

b) If mass of an object is increased four times​, $m_1=4m$

New force,

$F'=G\dfrac{m_1'm_2}{r^2}\\\\F=G\dfrac{4m_1m_2}{r^2}\\\\F'=4\times G\dfrac{4m_1m_2}{r^2}\\\\F'=4F$

New force will become 4 times of the initial force

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