A bomb of mass 30 ~kg at rest explodes into two pieces of masses 18 ~kg and 12 kg . The velocity of 18 ~kg mass is 6 ~ms^ -1 . The kinetic energy of the other mass is:

Correct answer: B. 486 ~J According to law of conservation of conservation of angular moments aligned 30 × 0 & =18 × 6+12 × V V & =-9 m / s aligned Negative sign indicates that both fragments move in opposite direction. aligned K.E. of 12 kg & =(1)/(2) mv^2 & =(1)/(2) × 12 × 81 & =486 J aligned

NEET 2005

Exam: NEET
Year: 2005
Subject: Physics
Chapter: Center of Mass, Momentum and Collision

NEET 2005 · Physics · Center of Mass, Momentum and Collision

A bomb of mass 30 ~kg at rest explodes into two pieces of masses 18...

A bomb of mass

30 \mathrm{~kg}

at rest explodes into two pieces of masses

18 \mathrm{~kg}

and 12

\mathrm{kg}

. The velocity of

18 \mathrm{~kg}

mass is

6 \mathrm{~ms}^{-1}

. The kinetic energy of the other mass is:

Options

A $324 \mathrm{~J}$
B $486 \mathrm{~J}$
C $256 \mathrm{~J}$
D $524 \mathrm{~J}$

Correct answer

B. $486 \mathrm{~J}$

Step-by-step solution

According to law of conservation of conservation of angular moments

\begin{aligned} 30 \times 0 & =18 \times 6+12 \times V \\ \Rightarrow V & =-9 \mathrm{ m} / \mathrm{s} \end{aligned}

Negative sign indicates that both fragments move in opposite direction.

\begin{aligned} \text{K.E. of } 12 \mathrm{ kg} & =\frac{1}{2} \mathrm{mv}^2 \\ & =\frac{1}{2} \times 12 \times 81 \\ & =486 \mathrm{ J} \end{aligned}

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