First slide

Law of conservation of momentum and it's applications

Question

A body of mass 5 kg explodes at rest into three fragments with masses in the ratio 1 : 1 : 3. The fragments with equal masses fly in mutually perpendicular directions with speeds of 21 m/s. The velocity of the heaviest fragment will be

Moderate

A

11.5 m/s
B

14.0 m/s
C

7.0 m/s
D

9.89 m/s

Solution

$P_{x} = m \times v_{x} = 1 \times 21 = 21 kg m / s$
$P_{y} = m \times v_{y} = 1 \times 21 = 21 kg m / s$
$∴$ Resultant = $\sqrt{P_{x}^{2} + P_{y}^{2}} = 21 \sqrt{2}$ kg m/s
The momentum of heavier fragment should be numerically equal to resultant of ${\vec{P}}_{x}$ and ${\vec{P}}_{y}$ .
$3 \times v = \sqrt{P_{x}^{2} + P_{y}^{2}} = 21 \sqrt{2} ∴ v = 7 \sqrt{2}$ = 9.89 m/s

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