Question

A bomb of mass 16kg at rest explodes into two pieces of masses 4kg and 12kg. The velocity of the 12kg mass is 4m/s. The kinetic energy of the other mass is : (a) (b) 96j (c) 144j (d) 288j

Answer 1

This involves the following concept : The law of conservation of momentum .

In the first step we'll use the formula to find the velocity of the object with mass 4 Kg .

$mu = m1v1 + m2v2 \\ initially \: th \: bomb \: is \: at \: rest \: so \: \\ mu = 0 \\ m1v1 + m2v2 = 0 \\ (4v1) + (12 \times 4) = 0 \\ 4v1 = 12 \times 4 \\ v1 = 12m {s}^{ - 1} \\ here \: i \: removed \: the \: negative \: sign \: cz \: i \: knw \: its \: going \: in \: te \: opposite \: direction \: \\ now \: Kinetic \: energy \: = \\ 0.5m {v}^{2} \\ = 2 \times 144 = 288j$

so the answer is 288 J

Answer 2

Answer:288J

Explanation:

By conservation of linear momentum:

M1 V1 = M2 V2

So, V2 = M1 V1 / M2

V2 = 12 × 4 / 4

V2 = 12 m/s

Then we find kinetic energy

= 1/2 mv^2

= 1/2 × 4 × (12)^2

= 288J