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.
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 ?
Asked in UPSC CAPF 2010 · Topic: Mechanics (Work, Energy, and Power)
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