Question

Three small spheres of mass M, 2M and 4M are kept in a straight line as shown. The distance between M and 2M is 6 meters. Find the distance x between 2M and 4M such that the sphere 2M is in equilibrium.

Answer 1

Explanation:

so here we know the masses which are M ,2M

and distance b/w them = 6m

so gravitational force will be

= G (M1) (M2)/ d^2

= G (2M)(M) / (6)^2

= 2M^2 ×G / 36

= GM^2 /18

now here mass 2M should be in equilibrium

so force applied on this mass from mass 4M should also be equal to force applied by mass M

so masses are 2M and 4M

and distance b/w them is X m

so and force = GM^2/18

now ,

G (2M)(4M) / X^2 = GM^2/ 18

8GM^2 × 18 / GM^2 = X^2

144 = X^2

X= 12 m answer

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