Question

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Answer 1

We know the relation between the force acting on a body, the mass of the body and the acceleration on the body thus produced, by Newton's Second Law of Motion.

$F=ma\\\\\\a=\dfrac {F}{m}$

For a constant force F, we get that,

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

I.e., if two bodies of different masses undergo same force, then the accelerations produced on the bodies are inversely proportional to their masses. Hence for bigger mass, smaller acceleration is produced.

Also, from this relation we can make the following equation.

$\dfrac {a_1}{a_2}=\dfrac {m_2}{m_1}\quad\longrightarrow\quad (1)$

Here we're given that,

$\dfrac {m_1}{m_2}=\dfrac {3}{4}$

where $m_2$ is the bigger mass. Then,

$\dfrac {a_1}{a_2}=\dfrac {4}{3}$

But given, $a_2=12\ m\ s^{-2}.$ So,

$\dfrac {a_1}{12}=\dfrac {4}{3}\\\\\\a_1=12\times\dfrac {4}{3}\\\\\\a_1=\mathbf {16\ m\ s^{-2}}$

Hence $\mathbf {16\ m\ s^{-2}}$ is the mass of the other body.

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