Question

At high altitude a body at rest explodes into two fragments of equal masses, with one fragment receiving horizontal velocity of $10m{s}^{-1}$. Time taken by the two radius vectors connecting to point of explosion to both the fragments to make ${90}^0$ is $(g=10m{s}^{-1})$

• A. $10s$
• B. $4s$
• C. $2s$
• D. $1s$

Answer 1

The correct option is D $1s$

Initial Momentum of the system is zero.
So just after the blast momentum of the system will be zero hence particle will move in the opposite direction
such that

$M_1{V}_1=M_2{V}_2$

because $M_1=M_2$ hence $V_1=V_2$

So when their velocity vectors are perpendicular to each other then dot product of their velocity will be zero
hence

$(-10\hat{i}-gt\hat{j}).(10\hat{i}-gt\hat{j})=0$
hence

$t=\frac{\sqrt{10\times 10}}{g}=1sec$