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.

Options

A. 320 N
B. 640 N
C. 180 N
D. 360 N

Answer

C

Explanation

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`