An aluminium sphere is immersed in water at 10^ C . If the temperature is increased, the force of buoyancy

Step-by-step solution

The buoyant force on the completely immersed sphere is given by F_B = V _w g , where V is the volume of the aluminium sphere and _w is the density of water. When the temperature is increased by T , the new volume of the sphere becomes V' = V(1 + _ Al T) and the new density of water becomes _w' = _w 1 + _w T , where _ Al and _w are the coefficients of volume expansion of aluminium and water respectively. The new buoyant force is F_B' = V' _w' g = V _w g ( 1 + _ Al T 1 + _w T ) . Since the coefficient of volume expan