A bucket containing water is tied to one end of a rope of length 2.5 m and rotated about the other end in a vertical circle so that water does not spill even when bucet is upside down . What is the maximum velocity of the bucket at which this happens ? How many rotations per minute is it making `g = 10 m//s^(2) ` .

A bucket containing water is tied to one end of a rope of length 2.5 m

1.	A bucket containing water is tied to one end of a rope of length 2.5 m and rotated about the other end in a vertical circle so that water does not spill even when bucet is upside down . What is the maximum velocity of the bucket at which this happens ? How many rotations per minute is it making `g = 10 m//s^(2) ` .
Answer» Here, ` = 2.5 m`.Water in the bucket will not spill when weight of water is balanced by centrifugal force , `mg = (m upsilon^(2))/(r)`, `upsilon = sqrt(rg) = sqrt(2.5 xx 10 ) = 5 m//s ` This is the velocity at the highest point Angular speed , `omega = (upsilon)/(r) = (5)/(2.5) = 2 rad //s ` Frequency of rotation `n = (omega)/(2pi) = (2)/(2 pi) rps = (60)/(pi) "rpm"`

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