First slide
Conservation of mechanical energy
Question

A small sphere is given vertical velocity of magnitude v0=5ms-1 and it swings in a vertical plane about the end of a massless string. The angle θ with the vertical at which string will break, knowing that it can withstand a maximum tension equal to twice the weight of the sphere, is

Moderate
Solution

from equation of motion, v2 = v02+2gl cos θ for vertical circular motion tension in string is T= mg cos θ+  mv2l m is mass attached to string, g is acceleration due to gravity,  θ is angle made by string with vertical, v is velocity of mass, l is length of string Given string can withstand tension T = 2mg  , substitute in above equation                             2mg = mg cos θ+ml(v02+2gl cosθ)   on simplification   cos θ =14  angle made by the string with vertical θ=cos-1(14)

 

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