First slide

Third law

Question

An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass 1 kg moves with a speed of $12 m s^{- 1}$ and the second part of mass 2 kg moves with $8 m s^{- 1}$ speed. If the third part flies off with $4 m s^{- 1}$ speed, then its mass is

Moderate

A

7 kg
B

17 kg
C

3 kg
D

5 kg

Solution

The situation is as shown in the figure.
According to law of conservation of linear momentum
${\bar{p}}_{1} + {\bar{p}}_{2} + {\bar{p}}_{3} = 0 ∴ {\bar{p}}_{3} = - ({\bar{p}}_{1} + {\bar{p}}_{2}) H e r e {\bar{p}}_{1} = (1 k g) (12 m s^{- 1}) \hat{i} = 12 \hat{i} k g m s^{- 1} {\bar{p}}_{2} = (2 k g) (8 m s^{- 1}) \hat{j} = 16 \hat{j} k g m s^{- 1} ∴ {\bar{p}}_{3} = - (12 \hat{i} + 16 \hat{j}) k g m s^{- 1} T h e m a g n i t u d e o f {\bar{p}}_{3} i s {\bar{p}}_{3} = \sqrt{{(12)}^{2} + {(16)}^{2}} = 20 k g m s^{- 1} ∴ m_{3} = \frac{p_{3}}{v_{3}} = \frac{20 k g m s^{- 1}}{4 m s^{- 1}} = 5 k g$

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