Question

If the kinetic energy of a body becomes four times of its initial value, then the new momentum will be

• A. double
• B. 3 times
• C. 4 times
• D. unchanged

Answer 1

Answer: (A)

double

The kinetic energy of the body is given by

$E=\frac{1}{2}m(v{)}^2$

$E=\frac{1}{2m}{m}^2(v{)}^2$

$E=\frac{p^2}{2m}$ ......(1)

Now, the kinetic energy of a body becomes four times of its initial value, then

$4E=\frac{{\left(p^{{}^{\prime }}\right)}^2}{2m}$...........(2)

Comparing equations (1) and (2)

$\frac{2m{p}^{\prime 2}}{2m{p}^2}=\frac{4E}{E}$

$\frac{p^{\prime 2}}{p^2}=\frac{4}{1}$

$\therefore \frac{p^{\prime }}{p}=\frac{2}{1}$

$\therefore p^{{}^{\prime }}=2p$