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

$$T = 2\pi\sqrt{L/g}$$. $$T_1 = 10/20 = 0.5$$s. $$T_2 = 10/40 = 0.25$$s. $$T_2/T_1 = 1/2 = \sqrt{L_2/L_1}$$. $$L_2 = L_1/4 = 30/4 = 7.5$$ cm.

The answer is Option 4: 7.5 cm.

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