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UPSC Civil Service Exam Questions

Q1:
A smooth sphere of weight W is supported in contact with a smooth vertical wall by a string fastened to a point on its surface, the other end being attached to a point in the wall as shown in the given figure. If the length of the string is equal to the diameter of the sphere, then the tension in the string and the reaction of the wall respectively will be

A
4W/3, 2W/3

B
2W/3, W/3

C
5W/3, W/3

D
3W/3, W/3

ANS:B -

2W/3, W/3

Here ,lenght of string ,oc=2r.
The radius of the sphere, oA=r.

In AOC,sinC=oA/OC=r/2r=1/2
C=30degree,AOC=60,
Tcsin60=W.
Tc(√3/2)=w.
TC=2W/√3.
THEN ,R=Tccos60.
R=TC/2(previously TC=2w/√3,substitute here).
R=w/√3.



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