Final answer:
The kinetic energy of a body will become eight times its original value when its mass is quadrupled and velocity is doubled, according to the formula KE = (1/2)mv^2, making option D correct.
Step-by-step explanation:
To determine the change in the kinetic energy of a body when its mass is quadrupled (made four times) and its velocity is doubled, we can use the kinetic energy formula:
KE = (\frac{1}{2}mv^2\)
Where:
- m is the mass of the object.
- v is the velocity of the object.
Let's assume the initial kinetic energy of the body is KE1 with mass m and velocity v. After the changes, the new kinetic energy KE2 will be with mass 4m and velocity 2v.
KE2 = (\frac{1}{2} \times 4m \times (2v)^2\)
KE2 = (\frac{1}{2} \times 4m \times 4v^2\)
KE2 = 8 \(\frac{1}{2} mv^2\) which is 8 times the original kinetic energy KE1.
Therefore, the kinetic energy of the body will become eight times its original value. The correct option is D. Eight times.