A cylindrical block of wood (density = 650kg m ^ - 3 ), of base area 30 cm ^ 2 and height 54cm , floats in a liquid of density 900kg m ^ - 3 . The block is depressed slightly and then released. The time period of the

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Quantrex Academy · Accepted Answer

Correct answer: C. 39cm

Case-I In equilibrium F _ up = mg V _ i ρ _ L g = mg Ah ρ _ L g = AL ρ _ s g (1) Case-II Let block is pressed by x more in liquid F _ net = F _ up ^ 1 - mg = V _ i ^ 1 ρ _ L g - mg F _ net = A(h + x) ρ _ L g - AL ρ _ s g F _ net = Ah ρ _ L g + Ax ρ _ L g - AL ρ _ s g . . . . . . . . . . (2) from equation (1) & (2) F _ net = Ax ρ _ L g restoring force in upward direction α = F _ net m = ( A ρ _ L g A ρ _ s L )x α = ω ^ 2 x for SHM and ω ^ 2 = (g)/(l) so (g)/(l) = ρ _ L g ρ _ s L so l = ρ _ s L ρ _ L = (650 × 54)/(900) = 39cm

A cylindrical block of wood (density = 650kg m ^ - 3 ), of base...

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