Work Energy and Power - Result Question 56
59. An explosion blows a rock into three parts. Two parts go off at right angles to each other. These two are, $1 kg$ first part moving with a velocity of $12 ms^{-1}$ and $2 kg$ second part moving with a velocity of $8 ms^{-1}$. If the third part flies off with a velocity of $4 ms^{-1}$, its mass would be:
(a) $7 kg$
(b) $17 kg$
(c) $3 kg$
(d) $5 kg$
[2009]
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Answer:
Correct Answer: 59. (d)
Solution:
- (d) Momentum of first part
$\Rightarrow 1 \times 12=12$
Momentum of second part
$\Rightarrow 2 \times 8=16$
Resultant momentum,
$ =\sqrt{(12)^{2}+(16)^{2}}=20 $
Then $M_1$ be the mass of third part,
$ \begin{aligned} & M \cdot 4=20 \\ & M=\frac{20}{4}=5 kg \end{aligned} $
Let two parts of the rock move along $x$-axis and $y$ axis respectively.
If $M$ and $v$ be the mass and velocities of third part then
$Mv \cos \theta=12$
Mv $\sin \theta=16$
$\tan \theta=\frac{16}{12}=\frac{4}{3}$
$\cos \theta=\frac{3}{5}$
$v=4 m / s$
$M=\frac{12}{v \cos \theta}$
$M=\frac{12 \times 5}{4 \times 3}=\frac{60}{12}=5 kg$
