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A light pointer fixed to one prong of a tuning fork touches a vertical plate. The fork is set vibrating and the plate is allowed to fall freely. If eight oscillations are counted when the plate falls through 10 cm, the frequency of the tuning fork is

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360 Hz

280 Hz

56 Hz

560 Hz

answer is D.

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Detailed Solution

Time of fall = $\sqrt{\frac{2 h}{g}} = \sqrt{\frac{2 \times 10}{1000}} = \frac{1}{\sqrt{50}}$
In this time number of oscillations are eight.
So time for 1 oscillation = $\frac{1}{8 \sqrt{50}}$
Frequency = $8 \sqrt{50} Hz = 56 Hz$

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