Two bodies A and B having masses m and 4m respectively are moving with equal linear momentum. The ratio of kinetic energies between A and B is

The kinetic energy (K) of a body is related to its linear momentum (p) and mass (m) by the formula K = p² / (2m). In this problem, two bodies A and B have masses m and 4m respectively, and they move with equal linear momentum (p_A = p_B = p). For body A, the kinetic energy is K_A = p² / (2m). For body B, the kinetic energy is K_B = p² / (2 * 4m) = p² / (8m). To find the ratio of their kinetic energies (K_A: K_B), we divide K_A by K_B: (p² / 2m) / (p² / 8m). This simplifies to 8m / 2m, which equals 4 / 1. Therefore, the ratio of the kinetic energy of body A to body B is 4: 1, indicating that the lighter body possesses higher kinetic energy when momentum is constant.