Work Energy and Power - Result Question 43
46. An object flying in air with velocity $(20 \hat{i}+25 \hat{j}-12 \hat{k})$ suddenly breaks into two pieces whose masses are in the ratio $1: 5$. The smaller mass flies off with a velocity $(100 \hat{i}+35 \hat{j}+8 \hat{k})$. The velocity of the larger piece will be
[NEET Odisha 2019]
(a) $-20 \hat{i}-15 \hat{j}-80 \hat{k}$
(b) $4 \hat{i}+23 \hat{j}-16 \hat{k}$
(c) $-100 \hat{i}-35 \hat{j}-8 \hat{k}$
(d) $20 \hat{i}+15 \hat{j}-80 \hat{k}$
Show Answer
Answer:
Correct Answer: 46. (b)
Solution:
- (b) $ \vec{P} _i= \vec{P} _f$
$ \begin{aligned} & m \vec{v} _i=(\frac{m}{6} \vec{v} _1+\frac{5 m}{6} \vec{v} _2) \\ & \vec{v} _i=(\frac{ \vec{v} _1}{6}+\frac{5}{6} \vec{v} _2) \\ & 20 \hat{i}+25 \hat{j}-12 \hat{k}=\frac{(100 \hat{i}+35 \hat{j}+8 \hat{k})}{6}+\frac{5 \vec{v} _2}{6} \\ & \vec{v} _2=\frac{20 \hat{i}+115 \hat{j}-80 \hat{k}}{5} \\ & \therefore \quad \vec{v} _2=4 \hat{i}+23 \hat{j}-16 \hat{k} \end{aligned} $
