Question

A bucket raised from a well by means of a rope which is wound to a wheel of diameter 77cm. Given that the bucket ascents in 1 minute 28 seconds with a uniform speed of 1.1 m/s, calculate the no of complete revolutions the wheel makes in raising the bucket.

Answer 1

$d=77cmr=\frac{77}{2}cm$
t=1min.28sec = 88 sec Speed =1.1 m/s
Distance covered = $\pi dN$ where N is in r.p.s.
Also $\Rightarrow Speed\times time=distance=1.1\times 88$
$\therefore 1.1\times 88=\frac{22}{7}\times 77\times N$
$\Rightarrow N=\frac{1.1\times \text{/}{88}^8\times \text{/}7}{22\times \text{/}{77}_{11}}=\frac{\text{/}11\times not{8}^4}{\text{/}{22}_2\times 10}=\frac{4}{10}r.p.s$
$\Rightarrow N=\frac{4}{10}\times 60$ r.p.m. [r.p.s - revolution per second]
$\Rightarrow N=24$ r.p.m. [r.p.m - revolution per minute].
Distance covered = $\pi dN$ because
1 revolution covers $2\pi r$ or $\pi D$ distance.
Hence, N revolution covers $\pi DN$ distance.