question_answer

A body of mass 2 kg makes an eleastic collision with a second body at rest and continues to move in the original direction but with one fourth of its original speed. What is the mass of the second body? [JEE Main 9-4-2019 Morning]

A) 1.8 kg

B) 1.2 kg

C) 1.5 kg

D) 1.0 kg

Correct Answer: B

Solution :

[b]

By conservation of linear momentum :-

\[2{{\text{v}}_{0}}=2\left( \frac{{{\text{v}}_{0}}}{4} \right)+m\text{v}\Rightarrow \text{2}{{\text{v}}_{0}}=\frac{{{\text{v}}_{0}}}{2}+m\text{v}\]

\[\Rightarrow \frac{\text{3}{{\text{v}}_{0}}}{2}=m\text{v}\] .(1)

Since collision is elastic\[\to \]

\[{{\text{V}}_{\text{separation}}}\text{=}\,{{\text{v}}_{\text{approch}}}\]

\[\Rightarrow \text{v-}\frac{{{\text{v}}_{0}}}{4}={{\text{v}}_{0}}\Rightarrow \frac{\text{5}{{\text{v}}_{0}}}{4}=\text{v}\] ..(2)

equating (2) and (1)

\[\frac{\text{3}{{\text{v}}_{0}}}{2}=m\left( \frac{\text{5}{{\text{v}}_{0}}}{4} \right)\Rightarrow \,=m=\frac{6}{5}=1.2kg\]

Option [b]