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InterviewSolution
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A solid sphere of radius `R` is floating in a liquid of density `sigma` with half of its volume submerged. If the sphere is slightly pushed and released , it starts axecuting simple harmonic motion. Find the frequency of these oscillations.A. `(1)/(2pi) sqrt((3g)/(2R))`B. `(1)/(2pi) sqrt(2R)/(3g)`C. `(1)/(2pi)sqrt((R )/(g))`D. `(1)/(2pi)sqrt((5g)/(3R))` |
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Answer» Correct Answer - A Half of the volume of sphere is submerged. For equilibrium of sphere, Weight =upthrust `:. Vr_(x)g =(V)/(2) (r_(L)) (g), r_(s) =(rho_(L))/(2) ..(1)` When slightly pushed downwards by `x`, weigth will remain as it is while upthrust will increase. The increased upthrust will become the net restoring force (upwards). `F =-("extra upthrust")` `=- ("extra volume immersed") (r_(L)) (g)` or `ma =- (piR^(2)) xr_(L) (a= "acceleration")` `:. (4)/(3)piR^(3) ((rho)/(2))a =- (piR^(2)) xr_(L)g (a= "acceleraiton")` `:. a =- ((3g)/(2R))x` as the given motion is simple harmonic Frequency of oscillation, `f = (1)/(2pi) sqrt(|(a)/(x)|) =(1)/(2)sqrt((3g)/(2R))` |
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