Question

If momentum of a body increased by $50\%$, its kinetic energy will increased by

• A. $50\%$
• B. $100\%$
• C. $125\%$
• D. $150\%$

Answer 1

The correct option is C $125\%$

Suppose the original momentum of the body to be ‘p’ and a $50$% increase leads to amomentum of $p+\frac{50}{100}p=1.5p$

The relation between momentum ‘p’ and kinetic energy ‘k’ is $p^2=2km$ (m is mass of object) hence $k=\frac{p^2}{2m}$

New kinetc energy

$k^{\prime }=\frac{(1.5p{)}^2}{2m}$ ( as new p is 1.5p)

$k^{\prime }=2.25\times \frac{\left(p^2\right)}{2m}=2.25\times k$

$\%$ Increment in Kinetic energy $=\frac{k^{\prime }-k}{k}\times 100=\frac{2.25k-k}{k}\times 100=125\%$

So, kinetic energy increased by $125$%