JEE Main · 2019 · 11 Jan 2019 · Shift 2 · Elasticity & SHM

A pendulum is executing simple harmonic motion and its maximum kinetic energy is

K_{1}

. If the length of the pendulum is doubled and it performs simple harmonic motion with the same amplitude as in the first case, its maximum kinetic energy is

K_{2}

then:

(A) $K_{2} = 2 K_{1}$ ✓ Correct
(B) $K_{2} = \frac{K _{1}}{2}$
(C) $K_{2} = \frac{K _{1}}{4}$
(D) $K_{2} = K_{1}$

Answer: (A)

Solution

The maximum kinetic energy of a swinging pendulum equals the fall in potential energy from the extreme to the lowest point,

K = m g ℓ (1 - cos θ)

, with

θ

the angular amplitude. Keeping the same amplitude

θ

but doubling the length doubles this drop, so

K_{2} = m g (2 ℓ) (1 - cos θ) = 2 K_{1}

JEE Main · 2019 · 11 Jan 2019 · Shift 2 · Single correct option

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