A body weight 50 ~g in air and 40 ~g in water. How much would it weight in a liquid of specific gravity 1.5 ?

Step-by-step solution

Weight of body in air, m₁=50 g=5 10⁻² ~kg Weight of body in water, m₂=40 ~g =4 10⁻² ~kg Buoyant force on the body, aligned F^ &=m₁ g-m₂ g &=g (m₁-m₂ ) &=g (5 10⁻²-4 10⁻² ) F^ &=10⁻² ~g ~N aligned But buoyant force is given as aligned F^ &=V g 10⁻² ~g &=V g 10⁻² &= V 10⁻² &=10³ ~V [From Eq. (i)] V &=10⁻⁵ ~m ³ [ =10³ ~kg / m ³ ] Loss of weight in liquid = _ l V g & [ _ l =1.5 ] W^ &=1.5 10⁻⁵ 10 =& 1.5 10³ 10⁻⁵ 10 =& 0.15 ~N aligned Loss of weight (in kg) = w^ g = 0.15 10 =0.015 ~kg =15 ~g Weight of body in water =50-