Question

A railway carriage of mass $8000\text{kg}$ is moving with the speed of $54\text{km/hr}$ and collides inelastically with the another stationary carriage of same mass. Find the loss in kinetic energy in this process.
(Assume perfectly inelastic collision)

• A. $600\text{kJ}$
• B. $500\text{kJ}$
• C. $350\text{kJ}$
• D. $450\text{kJ}$

Answer 1

The correct option is D $450\text{kJ}$

Given mass of railway carriage, $\left(m_1\right)=8000\text{kg}$
speed of railway carriage $1,\left(u_1\right)=54\text{km/hr}=15\text{m/s}$
Mass of railway carriage $2,\left(m_2\right)=8000\text{kg}$
Speed of railway carriage $2,\left(u_2\right)=0\text{m/s}$
By conservation of momentum
$m_1{u}_1+m_2{u}_2=(m_1+m_2)v$
$\Rightarrow v=\frac{m_1{u}_1}{m_1+m_2}=\frac{8000\times 15}{16000}=7.5\text{m/s}$
Loss in kinetic energy = K.E before collision - KE. after collision.
$=\frac{1}{2}{m}_1{u}_1^2-\frac{1}{2}(m_1+m_2)v^2$
$=\frac{1}{2}\times 8000\times (15{)}^2-\frac{1}{2}\times (16000)\times (7.5{)}^2$
$=4000\times 225-8000\times 56.25$
$=450\text{kJ}$