Question

a solid cube is first floating in a liquid .the coefficient of linear expansion of a cube is alpha and the coefficient of volume expansion of a liquid is gama .on increasing the temperature of (liquid plus cube-system) the cube will sink if

a)Gaama=3 alpha
b)Gaama greater than 3 alpha
c)Gaama less than 3 alpha
d)Gaama = 2 alpha

Answer 1

Answer:

The cube sinks, when the density of cube is greater than that of water.

Initially, since cube floats on water, we can take that density of cube = density of water.

ie, ρ₀ =  ρ'₀

(where, ρ is the density of cube and ρ' is the density of water)

Now, we know that fractional change in density

ρ = ρ₀( 1 - 3αΔT) -------> (1) (for cube)

ρ' = ρ'₀( 1 - γΔT) --------> (2) (for water)

since for cube to sink,

ρ > ρ'

ρ₀( 1 - 3αΔT) > ρ'₀( 1 - γΔT)

( 1 - 3αΔT) > ( 1 - γΔT)

-3αΔΤ > -γΔΤ

multiplying by -1 throughout, we get,

3αΔΤ < γΔΤ

3α < γ

This is the required answer. Please mark as brainliest if it helps.