A body initally travelling at $7 m s^{- 1}$ , triples its speed. If the change in its momentum is $200 k g m s^{- 1}$ , find the mass of the body.

12.78 k g

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13.28 k g

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13.78 k g

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14.28 k g

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Solution

The correct option is D $14.28 k g$
Given: initial velocity, $u = 7 m s^{- 1}$ , final velocity, $v = 3 u = 21 m s^{- 1}$ , change in momentum, $Δ p = 200 k g m s^{- 1}$ .

Let the mass of the body be $m$ . Then,
Inital momentum $= m u$
Final momentum $= m v$

Change in momentum,
$Δ p = F i n a l m o m e n t u m - I n i t i a l m o m e n t u m \Rightarrow Δ p = m v - m u = m (v - u) \Rightarrow m = \frac{Δ p}{(v - u)}$
$\Rightarrow m = \frac{200}{21 - 7} = 14.28 k g$
Therefore, the mass of the body is $14.28 k g$

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