Question

Two particles of masses $m_1$ and $m_2$, approach each other due to their mutual gravitational attraction only. Then,

• A. acceleration of both the particles are equal
• B. acceleration of the particle of mass $m_1$ is proportional to $m_1$
• C. acceleration of the particle of mass $m_1$ is proportional to $m_2$
• D. acceleration of the particle of mass $m_1$ is inversely proportional to $m_1$

Answer 1

Answer: (C)

acceleration of the particle of mass $m_1$ is proportional to $m_2$

The gravitational force acting between the two masses $m_1$ and $m_2$ is given by

$F_G=\frac{G{m}_1{m}_2}{l^2}$

Force on mass $m_1$

$F_1=\frac{G{m}_1{m}_2}{l^2}=m_1{a}_1$

Where, $a_1=$ acceleration

$\Rightarrow a_1=\frac{G{m}_2}{l^2}\Rightarrow a_1\propto m_2$

And similarly, $a_2\propto m_1$