A 12 kg bomb at rest explodes into two pieces of 4 kg and 8 kg. If the momentum of 4 kg piece is 20 Ns, the kinetic energy of the 8 kg piece is

Question

A 12 kg bomb at rest explodes into two pieces of 4 kg and 8 kg. If the momentum of 4 kg piece is 20 Ns, the kinetic energy of the 8 kg piece is (A) 25 J (B) 20 J (C) 50 J (D) 40 J

Tardigrade Admin · Accepted Answer

Key Idea Explosion causes internal forces so momentum of system is conserved.

m = 12 k g

u = 0

(rest)
Initial momentum

= m \times u = 0

Momentum of

4 k g

piece

= 20 N s

m_{1} \times v = 20

v = \frac{20}{4} = 5 m s^{- 1}

Applying conservation of momentum,

0 = m_{1} v + m_{2} v^{'} = 20 + 8 \times v^{'}

v^{'} = \frac{- 20}{8} = \frac{- 5}{2} m s^{- 1}

After explosion,
Then,

K E = \frac{1}{2} m v^{2}

= \frac{1}{2} \times 8 \times (\frac{5}{2})^{2}

= \frac{1}{2} \times 8 \times \frac{25}{4} = 25 J

Q. A 12kg bomb at rest explodes into two pieces of 4kg and 8kg. If the momentum of 4kg piece is 20Ns, the kinetic energy of the 8kg piece is

25 J

20 J

50 J

40 J

Q. A $12 k g$ bomb at rest explodes into two pieces of $4 k g$ and $8 k g$ . If the momentum of $4 k g$ piece is $20 N s$ , the kinetic energy of the $8 k g$ piece is