# A balloon filled with hydrogen has a volume of 1000 litres and its mass is 1 kg. what would be the volume of the block of very light material which it

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A balloon filled with hydrogen has a volume of 1000 litres and its mass is 1 kg. what would be the volume of the block of very light material which it can just lift? One litre of material has mass of 91.3 gram.
(Density of air = 1.3 gram//litre).

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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.