First slide

Third law

Question

A body of mass M at rest explodes into three pieces, two of which of mass M /4 each are thrown off in
perpendicular directions with velocities of 3 $m s^{- 1}$ and 4 $m s^{- 1}$ , respectively. The third piece will be
thrown off with a velocity of

Moderate

A

1.5 $m s^{- 1}$
B

2 $m s^{- 1}$
C

2.5 $m s^{- 1}$
D

3 $m s^{- 1}$

Solution

Momentum of one piece $= \frac{M}{4} \times 3$
Momentum of second piece $= \frac{M}{4} \times 4$
$∴$ Resultant momentum $= \sqrt{\frac{9 M^{2}}{16} + M^{2}} = \frac{5 M}{4}$
The third piece should also have the same momentum. Let its veIocity be $ν,$ then $\frac{5 M}{4} = \frac{M}{2} \times v \Rightarrow v = \frac{5}{2} = 2.5 {ms}^{- 1}$

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