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A cylindrical log of wood of height h and area of cross-section A floats in water. It is pressed and then released. Show that the log would execute S.H.M. with a time period. `T=2 πsqrt(m/(A ρg))` where m is mass of the body and ρ is density of the
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One end of a V-tube containing mercury is connected to a suction pump and the other end to atmosphere. The two arms of the tube are inclined to horizontal at an angle of 45° each. A small pressure difference is created between two columns when the suction pump is removed. Will the column of mercury in V-tube execute simple harmonic motion? Neglect capillary and viscous forces.Find the time period of
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A tunnel is dug through the centre of the Earth. Show that a body of mass ‘m’ when dropped from rest from one end of the tunnel will execute simple harmonic
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A simple pendulum of time period 1s and length l is hung from a fixed support at O, such that the bob is at a distance H vertically above A on the ground (Fig. ). The amplitude is o θ . The string snaps at` θ = θ_ 0 /2`. Find the time taken by the bob to hit the ground. Also find distance from A where bob hits the ground. Assume θ 0 to be small so that ` sinθ_0 and cos θ_0 =1`
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varun
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