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A uniform solid hemisphere of radius 10 ...


A uniform solid hemisphere of radius 10 m and mass 64 kg is placed with its curved surface on the smooth horizontal surface and a string AB of length 4 m is attached to point A on its rim as shown in the figure Find the tension in the string if hemisphere is in equilibrium.

A

320 N

B

640 N

C

180 N

D

360 N

Text Solution

Verified by Experts

The correct Answer is:
C

According the rotational equilibrium of the hemisphere we can write
`OC=(3R)/(8)` and `ON=R-L=6m`
`AN=sqrt(R^(2)-(R-L)^(2))=8m`
`TxxRcostheta-mg((3R)/(8))sintheta=0`
`T=(3mg tantheta)/(8)=(3xx64xx10xx6)/(8xx8)=180N`
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