A force of 10 N is applied to two bodies of different masses. Body 1 has mass, $M_{1} = 10 k g$ and body 2 has mass, $M_{2} = 15 k g$ . What is the ratio of the accelerations of bodies 1 and 2?

2:3

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1:2

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2:1

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3:2

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Solution

The correct option is D
3:2

Given, Force (F)= 10 N, $M_{1} = 10 k g$ , $M_{2} = 15 k g$ .

Let, $A_{1}$ and $A_{2}$ be the accelerations of bodies 1 and 2 respectively.

$F o r c e = M a s s \times A c c e l e r a t i o n$

or, $A c c e l e r a t i o n = \frac{F o r c e}{M a s s}$

Since force is constant (same for both the bodies), Acceleration is inversely proportional to the Mass.

$a c c e l e r a t i o n \propto \frac{1}{m a s s}$

$\frac{A_{1}}{A_{2}}$ = $\frac{M_{2}}{M_{1}}$

$\frac{A_{1}}{A_{2}}$ = $\frac{15}{10}$

$\frac{A_{1}}{A_{2}} = \frac{3}{2}$

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