Question

The kinetic energy of a body is increased by $21$%. What is the percentage increase in the linear momentum of the body?

• A. $20$%
• B. $10$%
• C. $30$%
• D. $5$%

Answer 1

The correct option is B $10$%

K.E${}_2$ = $\frac{121}{100}$ K.E${}_1$

$\frac{1}{2}$mv${}_2$${}^2$ = $\frac{1}{2}$mv${}_1$${}^2$

v${}_2$ = $\frac{11}{10}$v${}_1$ or mv${}_2$ = $\frac{11}{10}$mv${}_1$

${\rho }_2$ = $\frac{11}{10}$${\rho }_1$ i.e $\frac{{\rho }_2}{{\rho }_1}$ = $\frac{1}{10}$

$\frac{{\rho }_2-{\rho }_1}{{\rho }_2}$ $\ast$ 100 = $\frac{1}{10}$ $\ast$ 100 = 10

Hence the percentage increase in linear momentum is 10%