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 $\left(E_2\right)=4E$.
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
$\left(p_1\right)=mv$
Therefore new linear momentum $\left(p_2\right)=m\times 2v$
$=2mv=2p_1$