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A wheel having radius 10cm is coupled by a belt to another wheel of radius 30cm. $1^{st}$ wheel increases its angular speed from rest at a uniform rate of $1.57 {rads}^{- 2}$ . The time for $2^{nd}$ wheel to reach a rotational speed of $100 rev/min$ is ….(assume that the belt does not slip)

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20 sec

10 sec

1.5 sec

15 sec

answer is A.

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Detailed Solution

r_{1} = 0.1 {m,   r}_{2} = 0.3 m

$r_{1} ω_{1} = r_{2} ω_{2}$

$ω_{0} = 0$

$r_{1} (ω_{0} + α t) = r_{2} ω_{2}$

$N_{2} = 100 rev/m i n$

$10 \times 1.57 \times t = 30 \times 2 π \times \frac{100}{60}$

$t = 20 \sec$

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