A balloon filled with hydrogen has a volume of 1000 litres and has mass of 1kg. What would be the volume of the block of very light material which it can just lift? One litre of the material has a mass 91.3g and density of air is `1.3 g" ""litre"^(-1).`

Explanation

Let V and M be the volume and mass of the balloon respectively.
Let `upsilon_(1) , m_(1)` and `rho_(1)` be the volume , mass and density of the block to be filled.
Here, `V = 1000` litres`= 1000 xx 10^(-3)m^(3) = 1m^(3)`,
`rho_(1) = 91.3 g//litre = 91.3 kg m^(-3)`,
`rho_(a) = 1.3 g//litre = 1.3 kg m^(-3)`,
Total volume of the balloon and block = `V + upsilon_(1)`.
The volume of air displaced = `(V +upsilon_(1))`. If ` rho_(a)` is teh density of air, then weight of air displaced
The balloon can lift the block if
Weight of balloon and block = weight of air displaced
i.e., `(M+m_(1))g = (V + upsilon_(1)) rho_(a)g`
`or (M+upsilon_(1)rho_(1))g = (V+upsilon_(1))rho_(a)g`
This gives, `upsilon_(1) = (Vrho_(a)-M)/(rho_(1)-rho_(a)) = (1xx1.3-1)/(91.3 = 1.3) = 0.3/90 m^(3)`
`=(0.3 xx 1000)/(90) litre = 3.33litres`.