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Question

A small sphere is given vertical velocity of magnitude v0=5 ms1 and it swings in a vertical plane about the end of a massless string. The angle θ with the vertical at which the string will break, given that it can withstand a maximum tension equal to twice the weight of the sphere, is


  1. cos1(23)
  2. cos1(14)
  3. 60
  4. 30


Solution

The correct option is B cos1(14)
FBD of sphere:


Applying law of conservation of energy:
Loss in Potential Energy of sphere = Gain in Kinetic Energy of Sphere 
mv22mv2o2=mglcosθ
v2=v2o+2glcosθ(i)

From the FBD,
Tmgcosθ=mv2l
Given, Tmax=2mg
2mg=mgcosθ+ml(v20+2glcosθ) (substituting (i))
3mgcosθ+mv20l=2mg
Putting l=2 m,v0=5 m/s
3gcosθ=152cosθ=14
θ=cos1(14)

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