Question

A solid cube floats in water half immersed and h small vertical oscillations of time period `pi/5`s. Find the mass (in kg) (Take g=10m/`s^(2)`.
A. 4
B. 2
C. 1
D. 0.5

Answer 1

Correct Answer - A
Since, the cube is half immersed. The density of cube should be half the density of water, i.e. 500 kg `m^(-3)`.
`T = 2pi sqrt((m)/(rho_(w)Ag))" "(k = rho_(w)Ag)`
`(pi)/(5)=2pi sqrt((a^(3)xxrho)/(rho_(w)xxa^(2)xxg))`
`therefore" "(a rho)/(g rho_(w))=(1)/(100) rArr (a)/(20)=(1)/(100)rArr a = 0.2 m`
Now, `m = a^(3)rho = 4` kg