Question

Two objects, one 4 times as massive as the other, are approaching each other under their mutual gravitational

Answer 1

To Find :

The acceleration of the heavier object.

Solution :

Force of gravitation on lighter object by heavier object is :

$F = \dfrac{Gm(4m)}{100^2}$

Acceleration of lighter object is given by :

$a_s = \dfrac{4Gm}{100^2}\\\\m = \dfrac{50^2}{G}$          .....1)

Now, acceleration of heavier object when separation between them is 25 km :

$4ma_h = \dfrac{Gm(4m)}{25}\\\\a_h = \dfrac{Gm}{25}$.....2)

Putting value of m in equation 2, we get :

$a_h = \dfrac{G\times 50^2}{G \times 25}\\\\a_h = \dfrac{2500}{25}\\\\a_h = 100\ m/s^2$

Therefore, the acceleration of the heavier object is​ 100 m/s².