A body of mass $M$ at rest explodes into three pieces, two of which of mass $M/4$ each are thrown off in perpendicular directions with velocities of $3\, m/s$ and $4\, m/s$ respectively. The third piece will be thrown off with a velocity of .......... $m/s$
A body of mass $M$ at rest explodes into three pieces, two of which of mass $M/4$ each are thrown off in perpendicular directions with velocities of $3\, m/s$ and $4\, m/s$ respectively. The third piece will be thrown off with a velocity of .......... $m/s$
$1.5 $
$2.0$
$2.5$
$3.0$
A body of mass $M$ at rest explodes into three pieces, two of which of mass $M/4$ each are thrown off in perpendicular directions with velocities of $3\, m/s$ and $4\, m/s$ respectively. The third piece will be thrown off with a velocity of .......... $m/s$
Momentum of one piece $ = \frac{M}{4} \times 3$
Momentum of the other piece $ = \frac{M}{4} \times 4$
Resultant momentum $ = \sqrt {\frac{{9{M^2}}}{{16}} + {M^2}} = \frac{{5M}}{4}$
The third piece should also have the same momentum.
Let its velocity be $v$, then $\frac{{5M}}{4} = \frac{M}{2} \times v$
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