JEE Main 2026 — Jan 23, Shift 1 — Physics solution

JEE Main2026Jan 23, Shift 1Physics

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
$7.5$
D
$15$

Solution

Doubling the number of oscillations in the same time halves the period: $T^{'} = T /2$ .

Since $T \propto ℓ$ , halving the period means $ℓ^{'} = \frac{ℓ}{2}$ , so $ℓ^{'} = \frac{ℓ}{4}$ .

$∴ ℓ^{'} = \frac{30}{4} = 7.5 cm$ .

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