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The angular velocity and the amplitude of a simple pendulum are ω and a respectively. At a displacement x from the mean position, if its kinetic energy is T and its potential energy is V, then the ratio of T to V is

Asked in CBSE AIPMT 1991 · Kinetic, potential and total energy

• (1) (a²-x²ω²)/(x²ω²)
• (2) (x²ω²)/(a²-x²ω²)
• (3) (a²-x²)/(x²)
• (4) (x²)/(a²-x²)

Step-by-step solution

Why the other options are wrong

• (1) comes from subtracts x²ω², a squared speed, from a², a squared length; the two cannot be subtracted, and the ω² cancels out of the ratio anyway
• (2) comes from is the same mismatched expression inverted, and inverted it would be V/T rather than T/V
• (4) comes from is V/T: the potential share has been put on top, when the question asks for kinetic over potential

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