Question

7) A rope of length R has one end tied to a fixed point and the other end tied to a pail full of water. The pail of water of mass M is brought into vertical circular motion. The rope can sustain a tension of To and no more before breaking. a) What is the minimum speed of the pail at the top of the circle if no water is to spill out? What is the tension in the rope at that point? b) If the pail is in uniform circular motion, what is the minimum speed at which the rope will break and at what point in the circle will it break?

Please explain. Thanks.

Answer 1

on Vertcle circle,

apply the Condition at the top of the Circle

Wt of the water = Centrifugal force

let V be the mnimum Speed,

that at top point,

mg = mV^2/R

g is accelration due to gravity

V^2 = g R

V = sqrt(gR)

at Highest point, as string slackens

Tension will decreases

from SUm of Forces in Y direction = 0

T0 = (mv^2/R - mg)

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at bottom point

Tb + mv^2/R = mg

Tb = mg - mv^2/R

at top point

Ta = mv^2/R + mg

clealry Ta > Tb

hence it breaks at top point

velocity to break must be greater than > sqrt( gR)