Answer:
The kinetic energy (K.E.) of a body is directly proportional to the square of its linear momentum (p). If the kinetic energy becomes 4 times its initial value, it means the square of the linear momentum becomes 4 times its initial value.
Let's denote the initial linear momentum as \( p_i \) and the final linear momentum as \( p_f \).
Given that the kinetic energy becomes 4 times its initial value, we can express this as:
\[ K.E._f = 4 \times K.E._i \]
Since kinetic energy is directly proportional to the square of linear momentum, we have:
\[ (p_f)^2 = 4 \times (p_i)^2 \]
Taking the square root of both sides:
\[ p_f = 2 \times p_i \]
So, the final linear momentum is twice the initial linear momentum.
Therefore, the correct answer is option (c) Twice the initial value.
