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Question
A bucket containing water is tied to one end of a rope 5 m long and it is rotated in a vertical circle about the other end. Find the number of rotations per minute in order that the water in the bucket may not spill.
Solution
Given:
r = 5 m
To find: Rotations per minute
Formulae:
- v = `sqrt("rg")`
- v = rω
- n = `ω/(2pi)`
Calculation:
From formula (i),
v = `sqrt(5 xx 9.8) = sqrt49 = 7` m/s
From formula (ii) and (iii),
n = `"v"/(2pi"r") = (7 xx 7)/(2 xx 22 xx 5) = 4.9/22` r.p.s.
∴ Rotations per minute = `4.9/22 xx 60` = 13.37 r.p.m.
Rotations per minute in order that the water in the bucket may not spill is 13.37 r.p.m.
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