JEE Main · 2026 · 23 Jan 2026 · Shift 1 · Elasticity & SHM

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A simple pendulum of string length 30 cm performs 20 oscillations in 10 s. The length of the string required for the pendulum to perform 40 oscillations in the same time duration is ______ cm. [Assume that the mass of the pendulum remains same.]

(A)120
(B)0.75
(C)7.5✓ Correct
(D)15

Answer: (C)

Solution

For

20

oscillations in

10

s the period is

T_{1} = 0.5

s; for

40

oscillations in

10

s the period is

T_{2} = 0.25

s, half of

T_{1}

. Since

T \propto ℓ

\frac{T _{2}}{T _{1}} = \frac{ℓ _{2}}{ℓ _{1}}

, so

\frac{1}{4} = \frac{ℓ _{2}}{30}

and

ℓ_{2} = 7.5

cm.

JEE Main · 2026 · 23 Jan 2026 · Shift 1 · Single correct option

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