Question

The kinetic energy of a body is increased by 21%. What is increased in the momentum of the body.

A river of salty water is flowing with a velocity of 10 ms–1. If the density of the water is 1.2 gm/sc. Then the kinetic energy of each cubic metre of water is

Answer 1

Given that,

(a). Increment of kinetic energy $=21$%

We know that,

Initial kinetic energy is

$K.E_i=x$

$\frac{p_i^2}{2m}=x$

$p_i=\sqrt{2mx}$

Final kinetic energy is

$K.E_f=x+\frac{21}{100}x$

$\frac{p_f^2}{2m}=1.21x$

$p_f=\sqrt{1.21x\times 2m}$

Now,

$=\frac{p_f-p_i}{p_i}\times 100$

$=\frac{\sqrt{1.21x\times 2m}-\sqrt{x\times 2m}}{\sqrt{x\left(2m\right)}}\times 100$

$=\frac{\sqrt{2xm(1.21-1)}}{\sqrt{2xm}}\times 100$

$=(1.1-1)\times 100$

$=10$%

Hence, the increment in the momentum of the body is $10$%

(b). given that,

Velocity $v=10m/s$

The kinetic energy is

$K.E=\frac{1}{2}\times 1\times 10\times 10\times 1.2\times \frac{{10}^{-3}}{{10}^{-6}}$

$K.E=60KJ$

Hence, the kinetic energy is $60KJ$