Question

A body of mass 1 kg strikes elastically with another body at rest and continues to move in the same direction with one fourth the initial velocity. The mass of the other body is :

• A. $3kg$
• B. $0.8kg$
• C. $2.4kg$
• D. $4kg$

Answer 1

Answer: (B)

$0.8kg$

Body 1, initial velocity $=u$,

Final velocity $=u/4$

Body 2, initial velocity $=0$

Final velocity $v$

and mass $=m$

So, $1\times u+0=1\times \frac{u}{4}+mv$ [conservation of momentum]

$u=\frac{u}{4}+mv$ .......... (1)

Again $\frac{1}{2}\times 1\times u^2+0=\frac{1}{2}\cdot 1{\left(\frac{u}{4}\right)}^2+\frac{1}{2}m{v}^2$ [conservation of KE]

or, $\frac{u^2}{2}=\frac{u^2}{32}+\frac{1}{2}m{v}^2$

or, $15u^2=16m{v}^2$ ........... (2)

Solving equation (1) & (2) we get,

m $=$ $0.8kg$