X is twice as massive as Y. X also runs twice faster than Y. Which one

X is twice as massive as Y. X also runs twice faster than Y. Which one among the following is the ratio of kinetic energy of X and Y ?

1 : 8
8 : 1
4 : 1
2 : 1
This question was previously asked in
UPSC CAPF – 2010
The ratio of kinetic energy of X and Y is 8 : 1.
The kinetic energy (KE) of an object is given by the formula KE = ½ * m * v², where m is the mass and v is the velocity. Given that the mass of X (m_X) is twice the mass of Y (m_Y), so m_X = 2 * m_Y. Also, the velocity of X (v_X) is twice the velocity of Y (v_Y), so v_X = 2 * v_Y.
KE_X = ½ * m_X * v_X² = ½ * (2 * m_Y) * (2 * v_Y)² = ½ * 2 * m_Y * 4 * v_Y² = 8 * (½ * m_Y * v_Y²)
KE_Y = ½ * m_Y * v_Y²
The ratio KE_X / KE_Y = [8 * (½ * m_Y * v_Y²)] / [½ * m_Y * v_Y²] = 8 / 1. Thus, the ratio is 8:1.
Kinetic energy is a scalar quantity representing the energy of motion. It is directly proportional to the mass of the object and the square of its velocity. Doubling the velocity has a much greater impact on kinetic energy than doubling the mass.