Question

A body P of mass $1kg$ undergoes elastic collision with another body Q at rest. After collision, body P continues to move in the original direction with a speed of $\frac{1}{4}th$ of its initial speed. Mass of the other body Q is

• A. $0.06kg$
• B. $0.6gram$
• C. $600gram$
• D. $0.6kg$

Answer 1

The correct option is D $0.6kg$

we have formulae,

$m_1{u}_1+m_2{u}_2=m_1{v}_1+m_2{v}_2$

$1\times u_1+0=\frac{u_1}{4}+m_2{v}_2$

$\Rightarrow v_2=\frac{3u_1}{4m_2}$

$\frac{1}{2}\times 1\times u_1^2+\frac{1}{2}\times m_2\times 0=\frac{1}{2}\times 1\times \frac{u_1^2}{16}+\frac{1}{2}\times m_2\times v_2^2$

$\frac{u_1^2}{2}=\frac{u_1^2}{32}+\frac{1}{2}{m}_2{\left(\frac{3u_1}{4m_2}\right)}^2$

$\frac{15u_1^2}{32}=\frac{9u_1^2}{32m_2}$

$\Rightarrow m_2=\frac{9}{15}$

$\therefore m_2=0.6kg$