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A belt moves over two pulley $A$ and $B$ as shown in figure. The pulleys are mounted on two fixed horizontal axles. Radii of the pulleys $A$ and $B$ are $50 c m$ and $80 c m$ respectively. pulley $A$ is driven at constant angular acceleration of 0.8 rad/s² . The belt does not slide on either of the pulleys. How long does it take for the pulley $B$ to acquire an angular velocity of $10 r a d / s$ .

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$t = 10 s$

$t = 20 s$

$t = 0.5 s$

$t = 25 s$

answer is B.

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Detailed Solution

$ω = ω_{0} + α t \Rightarrow t = \frac{ω_{B} - ω_{B o}}{α_{B}}$ $ω_{B o} = 0, ω_{B} = 10 \frac{r a d}{s}$

$r_{A} α_{A} = r_{B} α_{B} \frac{0.8 \times 0.5}{0.8} = α_{B} α_{B} = 0.5 \frac{r a d}{s^{2}},$

we have $t = 20 s$

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