Question

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

• A. Same as the initial value
• B. Twice the initial value
• C. Thrice the initial value
• D. Half of its initial value

Answer 1

The correct option is B

Twice the initial value

Step 1: Given data:

$K{E}_1=4KE\dots \dots \dots \dots \dots \dots \left(1\right)$

A body's kinetic energy increases four times from its starting point.

Step 2: Formula used:

The kinetic energy $KE=\frac{1}{2}m{v}^2$

Where $m=$Mass of the body and $v=$Velocity of the body.

The momentum $P=mv$

Where $P=$Momentum and $m=$Mass of the body and $v=$Velocity of the body.

Therefore the relationship between the kinetic energy and linear momentum,

$P=\sqrt{2mKE}\dots \dots \dots \dots \dots \dots \left(2\right)$

Step 3: Calculating momentum

When the kinetic energy of the body becomes four times its initial value then

$$\begin{gathered} P_1=\sqrt{2mK{E}_1} \\ {P}_1=\sqrt{2m\left(4KE\right)} \\ {P}_1=\sqrt{8mKE} \\ {P}_1=2\sqrt{2mKE}\dots \dots \dots \dots \dots \dots \dots \dots \left(3\right) \end{gathered}$$

Step 4: Divide the equation(2) and (3).

$$\begin{gathered} \frac{P}{P_1}=\frac{\sqrt{2mKE}}{2\sqrt{2mKE}} \\ \frac{P}{P_1}=\frac{1}{2} \\ {P}_1=4P \end{gathered}$$

As a result, when a body's kinetic energy has increased by four times from its beginning value, its momentum has also doubled.

Hence, the correct option is B.