The relative density of a solid with respect to a liquid is $4/5$and relative density of the liquid with respect to water is $10/9$.The buoyant force exerted by a liquid on a solid immersed in it equal to the weight of the liquid displaced by the solid. Specific gravity of solid with respect to water is?
A. $18/25$
B. $8/9$
C. $0.56$
D.$1.8$

Hint: Let us first understand buoyant force by an easy example. When you lost your swimming goggles in the pool's deepest section and attempted to swim down to retrieve them. Swimming downward can be painful since the water wants to pull you back up to the surface. The buoyant force is the upward force exerted on surfaces immersed in fluids.

Complete step-by-step solution:Solution:
Before solving the problem let us first get some idea about specific gravity. The ratio of a substance's density to the density of a given reference material is known as relative density or specific gravity. For liquids, specific gravity is almost always determined in relation to the densest water; for gases, the reference is air at room temperature.
  $RD = \dfrac{{{\rho _{subs\tan ce}}}}{{{\rho _{reference}}}}$
  $RD = $Relative density
${\rho _{subs\tan ce}} = $density of the substance being measured
${\rho _{reference}} = $Density of the reference
Given:
Density of liquid with respect to water is given as:
$\dfrac{{{d_{liquid}}}}{{{d_{water}}}} = \dfrac{{10}}{9}$
${d_{liquid}} = \dfrac{{10}}{9} \times {d_{water}}$ [$Equation\_1$]
Relative density of solid with respect to liquid is given as:
 $\dfrac{{{d_{solid}}}}{{{d_{liquid}}}} = \dfrac{4}{5}$
${d_{solid}} = \dfrac{4}{5} \times {d_{liquid}}$
${d_{solid}} = \dfrac{4}{5} \times \dfrac{{10}}{9} \times {d_{water}}$
${d_{solid}} = \dfrac{8}{9} \times {d_{water}}$
 So , option (b) is correct.

Note: Positive buoyancy, negative buoyancy, and neutral buoyancy are the three forms of buoyancy.
The object floats due to positive buoyancy, which occurs when the submerged object is lighter than the fluid displaced.
Negative buoyancy occurs when the submerged object is denser than the displaced fluid, causing the object to sink.
When the weight of an immersed object equals the fluid displaced, neutral buoyancy occurs. The scuba diver's dive is an excellent example of neutral buoyancy.