SHMHard

Question

A cylindrical block of density ρ is partially immersed in a liquid of density 3ρ .The plane surface of the block remains is 60cm. The block performs SHM when displaced from its mean position. [Use g = 9.8 m/s2]

Options

A.the maximum amplitude is 20 cm
B.the maximum amplitude is 40 cm
C.the time period will be 2π/7 seconds.
D.none

Solution

When cylindrical block partically immersed
FB = mg ⇒ 3ρAyg = ρA(60 × 10-2)g
y = 20 cm
⇒ Maximum amplitude = 20 cm

Restoring force when it is slightly decreased by an amount of x.
F = - (ᐃVσg) = - (Aσg)x
⇒T =
= S

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