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NEET · Physics · STD 11 - 5. work,energy,power and collision
An object flying in alr with velocity \((20 \hat{\mathrm{i}}+25 \hat{\mathrm{j}}-12 \hat{\mathrm{k}})\) suddenly breaks in two pleces whose masses are in the ratio \(1: 5 .\) The smaller mass flies off with a velocity \((100 \hat{\mathrm{i}}+35 \hat{\mathrm{j}}+8 \hat{\mathrm{k}}) .\) The velocity of larger piece will be
- A \(4 \hat{\mathrm{i}}+23 \hat{\mathrm{j}}-16 \hat{\mathrm{k}}\)
- B \(-100 \hat{\mathrm{i}}-35 \hat{\mathrm{j}}-8 \hat{\mathrm{k}} \)
- C \(20 \hat{\mathrm{i}}+15 \hat{\mathrm{j}}-80 \hat{\mathrm{k}}\)
- D \(-20 \hat{\mathrm{i}}-15 \hat{\mathrm{j}}-80 \hat{\mathrm{k}}\)
Answer & Solution
Correct Answer
(A) \(4 \hat{\mathrm{i}}+23 \hat{\mathrm{j}}-16 \hat{\mathrm{k}}\)
Step-by-step Solution
Detailed explanation
Conservation of linear momentum, \(\mathrm{mv}_{0}=\frac{\mathrm{m}}{6} \overline{\mathrm{v}}_{1}+\frac{5 \mathrm{m}}{6} \overline{\mathrm{v}}_{2}\) \(\Rightarrow m(20 \hat{\imath}+25 \hat{\jmath}-12 \hat{k})=\frac{m}{6}(100 \hat{\imath}+35 \hat{\jmath}+8 \hat{k})+\frac{5 m}{6} \bar{v}_{2} \)
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