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A potentiometer wire AB as shown is 40 cm long of resistance $50 Ω m^{- 1};$ the free end of an ideal voltmeter is touching the potentiometer wire. What should be the velocity of the jockey as a function of time so that reading in voltmeter varies with time as $(2 \sin π t) ?$

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$20 π \sin π t c m s^{- 1}$

$10 π \cos π t c m s^{- 1}$

$20 π \cos π t c m s^{- 1}$

$10 π \sin π t c m s^{- 1}$

answer is D.

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Detailed Solution

$v_{P} = 2 [\frac{20 + x}{40}]$

$v_{Q} = 2$

$v_{P} - v_{Q} = \frac{x}{10}$

$2 \sin π t = \frac{x}{10}$

$x = 20 \sin π t$

$\frac{d x}{d t} = (20 π \cos π t) c m s^{- 1}$

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