Work Energy and Power - Result Question 56

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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:

======= ####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:

3e0f7ab6f6a50373c3f2dbda6ca2533482a77bed:content/english/neet-pyq-chapterwise/physics/work-energy-and-power/work-energy-and-power—result-question-56.md (a) $7 kg$

(b) $17 kg$

(c) $3 kg$

(d) $5 kg$

[2009]

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Answer:

Correct Answer: 59. (d)

Solution:

  1. (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 $\sin \theta=16$

$\tan \theta=\frac{16}{12}=\frac{4}{3}$

$\cos \theta=\frac{3}{5}$

$v=4 m / s$

$M=\frac{12}{v \cos \theta}$

$M=\frac{12 \times 5}{4 \times 3}=\frac{60}{12}=5 kg$