Question

Two objects of mass 1kg and 2kg are placed at a distance of 1m. Find the ratio of acceleration of two bodies if only gravitational force is present in between them.​

Answer 1

Magnitude of the gravitational force acting between them are same for the two objects.

By Second Law of Motion, the acceleration of the object is,

$\sf{\longrightarrow a=\dfrac{F}{m}}$

At constant force, the acceleration is inversely proportional to the mass.

$\sf{\longrightarrow a\propto\dfrac{1}{m}}$

Here the ratio of masses of the objects is,

$\sf{\longrightarrow m_1:m_2=1:2}$

Hence ratio of their acceleration is,

$\sf{\longrightarrow a_1:a_2=\dfrac{1}{m_1}:\dfrac{1}{m_2}}$

$\sf{\longrightarrow a_1:a_2=\dfrac{m_1m_2}{m_1}:\dfrac{m_1m_2}{m_2}}$

$\sf{\longrightarrow a_1:a_2=m_2:m_1}$

$\sf{\longrightarrow\underline{\underline{a_1:a_2=2:1}}}$

Hence 2 : 1 is the answer.