Question

If the linear momentum of body increases by $20\%$ what will be $\%$ age increase in kinetic energy?

Answer 1

The momentum of a body is given by :
P = mv
P can be varied by varying either m or v. Since mass of a body is a constant quantity so we can change the momentum of a body by changing its velocity.
Momentum will be increased by $20\%$ if the velocity is changed by $20\%$, since its a linear relationship between the two.
Let
mass = m = 10kg
velocity = v = 100m/s
Momentum with these values = P = 1000 kgm/s
K.E with these values = K.E = 50000 J
After $20\%$ increase velocity becomes = v' = 120m/s
so new momentum = 1200 kgm/s
Change in momentum = $\frac{(1200-1000)}{1000}\times 100\%$
$=0.2\times 100\%$
$=20\%$
New K.E = 72000 J
$ChangeinK.E=\frac{(72000-50000)}{50000}\times 100\%$
$=0.44\times 100\%$
$=44\%$