A particle of mass 4 M which is initially at rest explodes into three pieces of masses M , M and 2 M . The equal masses move along X - and Y - axes with velocities 4   m   s - 1 and 6   m   s - 1 respectively. The magnitude of the velocity of the heavier mass is

Question

A particle of mass 4 M which is initially at rest explodes into three pieces of masses M , M and 2 M . The equal masses move along X - and Y - axes with velocities 4 &#160; m &#160; s - 1 and 6 &#160; m &#160; s - 1 respectively. The magnitude of the velocity of the heavier mass is

Aicharya · Accepted Answer

Recall the condition of conservation of linear momentum in $x -$ axis is,

$0 = M \times 4 + 0 + 2 M \times u \cos θ u \cos θ = 2 . . . (1)$

and a vertical component,

$0 = 0 + 6 M + 2 M u \sin θ u \sin θ = 3 . . . (2)$

from equation $(1) & (2)$

$\Rightarrow u^{2} \cos^{2} θ = 4 & u^{2} \sin^{2} θ = 9 \Rightarrow u^{2} \cos^{2} θ + u^{2} \sin^{2} θ = 13 \Rightarrow u^{2} = 13 \Rightarrow u = \sqrt{13} m s^{- 1}$

A particle of mass 4 M which is initially at rest explodes into three pieces of masses M , M and 2 M . The…

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