A horizontal platform with an object placed on it is executing S.H.M. in the vertical direction. The amplitude of oscillation is 4.0 x 10-3 m. What must be the least period of these oscillations, so that the object is not detached from the platform? (Take g = 10 m/s2)
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a
π25sec
b
π18sec
c
π14sec
d
π20sec
answer is A.
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Detailed Solution
By drawing free body diagram of object during the downward motion at extreme position, for equilibrium of massmg - R = mA (A = Acceleration)For critical condition R = 0so mg = mA ⇒ mg = mαω2 ⇒ω = ga = 104.0×10-3 = 50⇒T = 2πω = 2π50 = π25sec