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 ?

The kinetic energy (KE) of an object is defined by the formula KE = 1/2 mv², where 'm' is mass and 'v' is velocity [t2][t4]. According to the problem, object X is twice as massive as Y (m_x = 2m_y) and runs twice as fast as Y (v_x = 2v_y). Kinetic energy is directly proportional to the mass and to the square of the velocity [t5]. Therefore, the ratio of their kinetic energies is calculated as: KE_x / KE_y = (1/2 * m_x * v_x²) / (1/2 * m_y * v_y²). Substituting the given values: KE_x / KE_y = (2m_y * (2v_y)²) / (m_y * v_y²) = (2 * 4 * m_y * v_y²) / (m_y * v_y²) = 8/1. Thus, the ratio of the kinetic energy of X to Y is 8:1 [t1][t6].