Question

Which one of the following would a hydrogen balloon find easiest to lift:-
(A) one kg of steel
(B) one kg of lightly packed feathers
(C) one kg of water
(D) all the same

Answer 1

Hint:Object whose density is less would be easier to lift.The force exerted by the air to lift the balloon is called buoyant force or upthrust given by the formula
\[{f_b} = {\rho _a}Vg\].

Complete step by step answer:
As we can see from the question, the mass of all the objects is the same. So we might think the hydrogen balloon can lift everything with the same force. But no, even if the mass is the same, density will be different for different objects .Steel is more dense than water and water is more dense than feather. Now as we know density is mass per unit volume.
\[d = \dfrac{m}{V}\]
\[ \Rightarrow V = \dfrac{m}{d}\], which says volume and density are inversely proportional to each other when mass is constant. Since feathers have the lowest density, It will have the highest volume. And the upthrust required to lift balloon is \[{f_b} = {\rho _a}Vg\], Where \[{f_b}\] is the buoyant force or upthrust, \[{\rho _a}\]is the density of air and \[V\]is the volume of the object, \[g\]is acceleration due to gravity.Since density of air and acceleration due to gravity is the same all the time, Buoyant force will be more if the volume is more. Hence 1 kg of feather can be lifted by the hydrogen balloon easily.
Hence the correct option is B.

Note:Always remember that steel will be the hardest object to be lifted by the hydrogen balloon and buoyant force acts opposite to the weight of the object.