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4.1 , newtons laws of motion — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics4.1 , newtons laws of motion1 Mark
MCQ
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
    $1.5 $
  • B
    $2.0$
  • ✓
    $2.5$
  • D
    $3.0$
✓

Answer

Correct option: C.
$2.5$
c
(c) 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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