Question

The gravitational force between two objects is F. How will the force change when the mass of each object is quadrupled?

Answer 1

Answer

As F=G×M×m/r^2
where M is mass of 1st object
m is mass of 2nd object
now

F= G×4M×4m/r^2
F= 16 × G×M×m/r^2
so force will become 16 times
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Answer 2

Given:

• Gravitational force is F
• Mass of each object is m

To find:

• New Gravitational force ?

Calculation:

The general expression of gravitational force between two objects are:

$F = \dfrac{Gm_{1}m_{2}}{ {d}^{2} }$

Now, each of the mass is quadrupled (i.e. the masses becomes 4 times the initial value)

So, new force will be :

$F_{2}= \dfrac{G(4m_{1})(4m_{2})}{ {d}^{2} }$

$\implies F_{2}= \dfrac{16 Gm_{1}m_{2}}{ {d}^{2} }$

$\implies F_{2}= 16 \times \dfrac{ Gm_{1}m_{2}}{ {d}^{2} }$

$\implies F_{2}= 16 \times F$

So, the force becomes 16 times the initial value.