Exam

JEE Main

Year

2021

Date

31 August

Shift

Evening Shift

Subject

Physics

Chapter

Work, Power and Energy

JEE Main 2021 · 31 August · Evening Shift · Physics · Work, Power and Energy

A block moving horizontally on a smooth surface with a speed of 40m...

A block moving horizontally on a smooth surface with a speed of $40m{s}^{- 1}$ splits into two parts with masses in the ratio of $1: 2 .$ If the smaller part moves at $60m{s}^{- 1}$ in the same direction, then the fractional change in kinetic energy is :

Step-by-step solution

$m \times 40 = \dfrac{2}{3}mv + \dfrac{m}{3} \times 60$
$120 = 2v + 60$
$v = 30{\text{m s}}^{- 1}$
Now ${K}_{i} = \dfrac{1}{2} \times m \times {40}^{2} = 800m$
${K}_{f} = \dfrac{1}{2} \times \dfrac{2m}{3} ( 30{)}^{2} + \dfrac{1}{2} \times \dfrac{m}{3} \times ( 60{)}^{2}$
$= \dfrac{1}{6} { m ( 1800 + 3600 ) } = \dfrac{m ( 5400 )}{6} = 900m$
$\dfrac{\DeltaKE}{{K}_{i}} = \dfrac{900m - 800m}{800m} = \dfrac{1}{8}$