Question

the mass of a body is increased 4 fold and mass of other body is increased 16 fold how should the distance between them be changed to keep the same gravitation force between them​

Answer 1

The distance should be increased 8-fold.

Given:

mass of body 1 change = 4 times

mass of body 2 change = 16 times

To find: change in distance to keep F constant

Solution:

Let the initial mass of body 1 = m₁

Let the initial mass of body 2 = m₂

Let initial gravitational force = F₁

Let distance between the two bodies = r.

Now, F₁ = G$\frac{m_{1} m_{2} }{r^{2} }$

Now,

Changed mass of body 1 = 4m₁

Changed mass of body 2 = 16m₂

Final gravitational force = F₂

Changed distance = R (say)

F₂ = G$\frac{(4m_{1} )(16m_{2} )}{R^{2} }$

According to the question,

F₁ = F₂

⇒ G$\frac{m_{1} m_{2} }{r^{2} }$ = G$\frac{(4m_{1} )(16m_{2} )}{R^{2} }$

⇒ 1/r² = 64/R²

⇒ R² = 64r²

⇒ R = 8r

∴ The distance should be made 8-fold to keep the same gravitational force.

SPJ2