Question

A shell of mass $20\,kg$ at rest explodes into two fragments whose masses are in the ratio $2 : 3$. The smaller fragment moves with a velocity of $6 \,m/s$. The kinetic energy of the larger fragment is

• A. 360 J
• B. 144 J
• C. 216 J
• D. 96 J

Answer 1

Answer: (D)

96 J

Answer 2

Total mass of the shell $= 20 \,kg$
Ratio of the masses of the fragments = 2:3
$\therefore$ Masses of the fragments are $8 \,kg$ and $12 \,kg$
Now, according to the conservation of momentum
$m_1v_1=m_2v_2$
$8 \times 6=12 \times v$
v (velocity of the larger fragment) $=4\, m / s$
Kinetic energy $=\frac{1}{2} m v^{2}=\frac{1}{2} \times 12 \times(4)^{2}$
$=96\, J$