Question

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

• A. accelerations 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)

The gravitational force acting between the two masses $m_{1}$ and $m_{2}$ is given by
$F_{G}=\frac{G m_{1} m_{2}}{r^{2}}$
Force on mass $m_{1}$
$F_{1}=\frac{G m_{1} m_{2}}{r^{2}}=m_{1} a_{1}$
where, $a_{1}=$ acceleration
$\Rightarrow a_{1}=\frac{G m_{2}}{r^{2}}$
$\Rightarrow a_{1} \propto m_{2}$
and similarly, $a_{2} \propto m_{1}$