### Neet Solved Paper 2013 Question 7

##### Question: An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass 1 kg moves with a speed of 12 ms-1 and the second part of mass 2 kg moves with 8 ms-1 speed. If the third part flies off with 4 ms-1 speed, then its mass is

#### Options:

A) 3 kg

B) 5 kg

C) 7kg

D) 17kg

## Show Answer

#### Answer:

Correct Answer: B

#### Solution:

- We have $ p _1+p _2+p _3=0 $ $ [\because P=mv] $

$ \therefore $ $ 1\times 12i+2\times 8j+p _3=0 $

$ \Rightarrow $ $ 12i+16j+p _3=0 $

$ \Rightarrow $ $ p _3=-(12i+16j) $

$ \therefore $ $ p _3=\sqrt{{{(12)}^{2}}+{{(16)}^{2}}} $ $ \sqrt{144+256} $ $ =20kg-m/s $ Now, $ p _3=m _3v _3 $

$ \Rightarrow $ $ m _3=\frac{p _3}{v _3}=\frac{20}{4}=5kg $