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A uniform cylinder of length (L) and mass (M) having cross sectional area (A) is suspended, with its length vertical, from a fixed point by a massless spring, such that it is half - submerged in a liquid of density (rho) at equilibrium position. When the cylinder is given a small downward push and released it starts oscillating vertically with small amplitude. If the force constant of the spring is (k), the prequency of oscillation of the cylindcer is.A. `(1)/(2pi)[(K-Adg)/(M)]^(1//2)`B. `(1)/(2pi)[(K+Adg)/(M)]^(1/2)`C. `(1)/(2pi)[(K+Adg)/(M)]^(1//2)`D. `(1)/(2pi)[(K-Adg)/(M)]^(1/2)` |
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Answer» Correct Answer - C When the cylinder is given a downward push through a distance `y`, the restoring upward force in the spring `=-Ky.` Additional upward force due to buoyancy `=-Aydg.` Net upward restoring force, `F=-(ky+Aydg)` `=-(K+Adg)y` As, `F prop y` and it is directed towards equlibrium position, hence the cylinder will execute linear S.H.M. Here, spring factor `=(KAdg)` inertia factor`=` mass of cylinder `=M` Frequency, `v=(1)/(2pi)sqrt ((spr i ng fact o r)/(i n ertia fact o r))` `=(1)/(2pi)sqrt((K+Adg)/(M))` |
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