Question

Find the fraction of kinetic energy lost when the body of mass $M$ is jerked into motion

• A. $\frac{M}{M+m}$
• B. $\frac{M}{M-m}$
• C. $\frac{2M}{M+m}$
• D. $\frac{M}{2(M+m)}$

Answer 1

The correct option is A $\frac{M}{M+m}$

$u\to$ initial $v\to$ final

fraction of k.E lost $=$

$\frac{\frac{1}{2}m{u}^2-\frac{1}{2}(M+m)v^2}{\frac{1}{2}m{u}^2}$

$=1-\frac{M+m}{m}{\left(\frac{v}{u}\right)}^2$

$=1-\left(\frac{M+m}{m}\right){\left(\frac{m}{M+m}\right)}^2$

$=\frac{m}{M+m}$