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A body of mass (4m) is lying in x-y plane at rest. It suddenly explodes into three pieces. Two pieces, each of mass (m) move perpendicular to each other with equal speeds (v). The total kinetic energy generated due to explosion is:
A
$mv^2$
B
$\frac{3}{2}mv^2$
C
$2mv^2$
D
$4mv^2$
Detailed Solution
The third piece has mass 2m. By conservation of linear momentum: $2mv_1 = \sqrt2\,mv \Rightarrow v_1 = \frac{v}{\sqrt2}$
Total KE $= \frac{1}{2}mv^2 + \frac{1}{2}mv^2 + \frac{1}{2}(2m)v_1^2 = mv^2 + \frac{mv^2}{2} = \frac{3}{2}mv^2$
Total KE $= \frac{1}{2}mv^2 + \frac{1}{2}mv^2 + \frac{1}{2}(2m)v_1^2 = mv^2 + \frac{mv^2}{2} = \frac{3}{2}mv^2$