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

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

Infinity Learn · Accepted Answer

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$$+ml(v02+2gl$$ $$cos$$θ$$)$$   on simplification ⇒  $$cos$$ θ $$=14$$  angle made by the string with vertical θ$$=$$$$cos$$$$-1(14)$$

A small sphere is given vertical velocity of magnitude $v_{0} = 5 m s^{- 1}$ 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

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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

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A small sphere is given vertical velocity of magnitude $v_{0} = 5 m s^{- 1}$ 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