A wooden block in the form of a uniform cylinder floats with one-third length above the water surface. A small chip of this block is held at rest at the bottom of a container containing water to a height of `1 m` and is then released. The time in which it will rise to the surface of water is `=10 m//s^(2)`)

Options

A. ` 0.84 s `
B. ` 0.63 s `
C. ` 0 .5 s `
D. ` 1 s `

Answer

B

Explanation

From Archimedes Principle ` (2 V ) /(3) rho _L g = V rho _ b g rArr rho _L = (3)/(2) rho _b `
Acceleration of chip is given by ` V _ C rho _L g - V_Crho _b g = V_C rho _ b a `
` (3)/(2) rho _b g - rho _b g = rho _b a rArr a = ((1)/(2) g ) ` Hence ` 1 = (1)/(2) xx (g)/(2) xx t ^ 2 rArr t = sqrt ((4)/(10)) cong 0.6 ` sec