A cylindrical block of density p is partially immersed in a liquid of density 3p.The plane surface of the block remains parallel to the surface of the liquid.The height of the block is 60cm.The block performs SHM when displaced from its mean position(use: g=9.8 m/s^2).which are true?
- the maximum amplitude is 20cm
- the maximum amplitude is 40cm.
- the timeperiod will be 2pi/7
Asked by saraswatmajumder
16th March 2018,
12:33 AM
Answered by Expert
Answer:
if an object floats in a liquid, then its mass is same as the mass of displaced liquid.
Let h be height of cylinder below water level when it floats.
Then displaced liquid mass = h×A×(3p) ..................(1)
where A is corss section area of cylinder;
Mass of cylinder = 60×A×p ........................(2)
by equating (1) and (2) , we get h =20 cm.
let us calculate period of oscillation of SHM
a small displacement δh downwards will give an upward bouyance force F, due to this cylinder will be in SHM.
boyancy force F = δh×A×(p-3p)×g = -(2×A×p×g)×δh
hence for SHM, m×ω2 = 2×A×p×g ..................(1)
where ω is angular frequency of SHM
by substituting ω = (2π / T) and mass m = (A × 60 × p ) in above equation (1) we get T = 2π×(0.175)
hence time period is not matching with the time period ( 2π×(0.143) ) given in the question.
since the immersion height is 20 cm, only " maximum amplitude 20 cm " is true. All other statements are false
Answered by Expert
16th March 2018,
3:24 PM
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