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Relation between MA and VR

An explosion ...

Question

An explosion blows a rock into three parts. Two parts go off at right angles to each other. These two are $1 k g$ first part moving with a velocity of $12 m / s$ and $2 k g$ second part moving with a velocity of $8 m / s$ . If the third part flies off with a velocity of $4 m / s$ , its mass would be

5 k g

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7 k g

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3 k g

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17 k g

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Solution

The correct option is A $5 k g$
Draw a diagram of given situation.

Find the mass of third part.
Formula used: $p = m v$
Given,
$m_{1} = 1 k g$
$v_{1} = 12 m / s e c$
$m_{2} = 2 k g$
$v_{2} = 8 m / s e c$
$m_{3} = m$
$v_{3} = 4 m / s e c$
Momentum of first part,
$p_{1} = m_{1} v_{1} = 1 \times 12 = 12 k g m / s e c$
Momentum of second part,
$p_{2} = m_{2} v_{2} = 2 \times 8 = 16 k g m / s e c$
Resultant momentum of two parts is,
$\sqrt{(1 \times 12)^{2} + (2 \times 8)^{2}} = 20 k g m / s e c$
$∴ p_{3} = m_{3} v_{3} = 20 k g m / s e c$
Momentum of third part,
$20 = m \times 4 \Rightarrow m = 5 k g$
Final Answer: $(A)$

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Relation between MA and VR

Standard VIII Physics

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An explosion blows a rock into three parts. Two parts go off at right angles to each other. These two are 1 kg first part moving with a velocity of 12 m/s and 2 kg second part moving with a velocity of 8 m/s. If the third part flies off with a velocity of 4 m/s, its mass would be