Two objects, x and y, have equal mass and are moving with speeds u and

Two objects, x and y, have equal mass and are moving with speeds u and 3u respectively. Their kinetic energies k_x and k_y are related as

k_x = k_y
2k_x = k_y
9k_x = k_y
3k_x = k_y
This question was previously asked in
UPSC CAPF – 2022
The correct answer is C, 9k_x = k_y.
The kinetic energy (k) of an object with mass (m) and speed (v) is given by the formula k = ½ mv².
For object x, mass is m and speed is u, so k_x = ½ mu².
For object y, mass is m and speed is 3u, so k_y = ½ m(3u)² = ½ m(9u²) = 9 (½ mu²).
Comparing k_y with k_x, we find k_y = 9k_x, or 9k_x = k_y.
Kinetic energy is directly proportional to the mass of the object and the square of its speed. Doubling the speed of an object quadruples its kinetic energy (if mass remains constant). Tripling the speed increases the kinetic energy by a factor of nine.