Question

A particle of mass $100\text{g}$ moving with a speed $1\text{m/s}$ collides perfectly inelasticaly with another particle of mass $200\text{g}$ initially at rest. Find the loss in the kinetic energy of the system due to collision.

• A. 0.066 J
• B. 0.033 J
• C. 0.33 J
• D. 3.33 J

Answer 1

The correct option is B 0.033 J

Before collision

After collision

Using, law of conservation of momentum
$p_i=p_f{m}_1{u}_1+m_2{u}_2=(m_1+m_2)v$
$0.1\times 1=(0.1+0.2)v$
$\Rightarrow v=\frac{1}{3}\text{m/s}$
$\therefore$ Change in kinetic energy of system due to collision $\Delta k.E$ = $k_f-k_i$
$=\frac{1}{2}(m_1+m_2)v^2-\frac{1}{2}{m}_1{u}_1^2$
$=\frac{1}{2}\times 0.3\times {\left(\frac{1}{3}\right)}^2-\frac{1}{2}\times 0.1\times 1^2$
$=-0.033\text{J}$
$\therefore$ loss in kinetic energy of system due to collision is equal to $0.033\text{J}$