Question

Can a body have energy without having momentum and have momentum without having energy Explain?
The kinetic energy of a body is increased by 21%. What is percentage increase in the line momentum of the body.

Answer 1

Yes, a bucket of water of mass $m$ at height $h$ from the surface of ground have Potential Energy$mgh$.

But because it is in stationary condition, therefore it have zero momentum.

Hence, bucket have potential energy but its momentum is zero.

$E=$ Kinetic Energy

$P=$ Momentum

$E=\frac{1}{2}M{V}^2=\frac{{\left(MV\right)}^2}{2M}=\frac{P^2}{2M}$

$E_1=E$ ,

Kinetic Energy increase by $21$% $E_2=E+\frac{21}{100}E=\frac{121E}{100}$

$\frac{E_1}{E_2}=\frac{p_1^2}{p_2^2}$

$\frac{p_1}{P_2}=\sqrt{\frac{E_1}{E_2}}=\sqrt{\frac{100}{121}}=\frac{10}{11}$

$p_2=\frac{11}{10}{p}_1$$=p_1+\frac{1}{10}{p}_1=1.1P_1$

Hence, increase in momentum in $10$%.