Work Energy and Power - Result Question 50
53. A body of mass $(4 m)$ 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 :
[2014]
(a) $mv^{2}$
(c) $2 mv^{2}$
(b) $\frac{3}{2} mv^{2}$
(d) $4 mv^{2}$
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Answer:
Correct Answer: 53. (b)
Solution:
- (b) By conservation of linear momentum Magnitude of the momentum of heavier piece of mass $(2 m)=$ Magnitude of the vector sum of momentum of each piece of mass (m)
$ \begin{aligned} & (2 m) v_1=\sqrt{(m v)^{2}+(m v)^{2}} \\ \Rightarrow \quad & 2 m v_1=\sqrt{2} mv \Rightarrow v_1=\frac{v}{\sqrt{2}} \end{aligned} $
As two masses of each of mass $m$ move perpendicular to each other.
Total KE generated
$=\frac{1}{2} mv^{2}+\frac{1}{2} mv^{2}+\frac{1}{2}(2 m) v_1^{2}$
