Question

The kinetic energy of a body becomes four times its initial value. The new linear momentum will be

• A. same as the initial value
• B. four times of the initial value
• C. twice of the initial value
• D. eight times of the initial value

Answer 1

Answer: (C)

Initial kinetic energy $\left(E_{1}\right)=E$ and final kinetic energy $\left(E_{2}\right)=4 E$.
Kinetic energy of a body is $\frac{1}{2} m v^{2}$
Since the value of $m$ remains constant, therefore for the
kinetic energy to be $4$ times, the new value of velocity $(v)$
should be $2$ times the initial value. Initial linear momentum
$\left(p_{1}\right)=m v$
Therefore new linear momentum $\left( p _{2}\right)= m \times 2 v$
$ = 2\,mv = 2p_1$