Question

If the earth attracts two objects with equal force, can we say that their masses
must be equal?​

Answer 1

For Short Answer:-

The Earth attracts objects with a force which is referred as Weight. Since the force of attraction are same. We can say that the object has a same mass.

$Mathematically,$

Sure we can say that the masses of the objects are same.

Proof:-

• Let, the mass of the first object be = $m_1$
• Mass of the second object = $m_2$
• Mass of Earth = $M$
• Radius of the Earth = $R$

We know,

$F = G \frac{M \times m}{R^2}$

(Recall what is F, G, M, m and R)

For object 1:-

$F_1 = G \frac{M \times m_1}{R^2}$ ...(1)

For object 2:-

$F_2 = G \frac{M \times m_2}{R^2}$ ...(2)

As per question, $F_1 = F_2$.

From (1) and (2),

$G \frac{M \times m_1}{R^2} = G \frac{M \times m_2}{R^2}$

$\implies m_1 = m_2$

(After cancellation).

∴ Mass of the first object is same as the mass of the second one.