Question

A metal ball of mass $2kg$ moving with a velocity of $36$ km/h has a head on collision with a stationary ball of mass $3kg$. If after the collision, the two balls move together, the loss in kinetic energy due to collision is.

• A. $140J$
• B. $100J$
• C. $60J$
• D. $40J$

Answer 1

The correct option is C $60J$

Apply conservation of momentum,
$m_1{v}_1=(m_1+m_2)v$
$v=\frac{m_1{v}_1}{(m_1+m_2)}$
Here $v_1=36km/hr=10m/s$,
$m_1=2kg,m_2=3kg$
$v=\frac{10\times 2}{5}=4m/s$
K.E. (initial) $=\frac{1}{2}\times 2\times (10{)}^2=100J$
K.E. (Final) $=\frac{1}{2}\times (3+2)\times (4{)}^2=40J$
Loss in K.E. $=100-40=60J$
Alternatively use the formula
$-\Delta E_k=\frac{1}{2}\frac{m_1{m}_2}{(m_1+m_2)}(u_1-u_2{)}^2$