Question

The mass of a body is increased by $100$% and velocity of a body is decreased by $50$%. What is the percentage change in its kinetic energy?

• A. $50$%
• B. $100$%
• C. $75$%
• D. $150$%

Answer 1

The correct option is A $50$%

New mass $m^{\prime }=m+\frac{100}{100}\times m$

$m^{\prime }=m+m=2m$

New velocity $v^{\prime }=v-\frac{50}{100}\times v$

$=v-\frac{v}{2}$

$v^{\prime }=\frac{v}{2}$

New kinetic energy,$K.E^{\prime }=\frac{1}{2}{M}^{\prime }{V}^{\prime 2}$

$=\frac{1}{2}\times 20\times \frac{V^2}{4}=\frac{m{v}^2}{4}$

Initial kinetic energy$=\frac{m{v}^2}{2}=KE$

$K{E}^{\prime }=\frac{1}{2}KE=50$% of KE