A baloon a is filled with helium so that at the atmospheric temperature and pressure it has volume V

Question

A baloon a is filled with helium so that at the atmospheric temperature and pressure it has volume V . A baloon B is filled with hydrogen under the same conditions and it has volume V/2. When the baloons released\

Professor PC Thomas Classes · Answer

Acceleration $=\frac{	ext { upward Force }- 	ext { weight }}{	ext { total mass }}$ Acceleration of A is $\mathrm{a}_{\mathrm{A}}=\frac{\mathrm{Vdg}-\mathrm{V} 	imes 4 	imes \mathrm{g}}{\mathrm{V} 	imes 4}$\ where 4 stands for the density of helium\ Acceleration of $B$ is $a_{B}=\frac{\frac{V}{2} d g-\frac{V}{2} 	imes 2 	imes g}{\frac{V}{2} 	imes 2}$ Multiply and divide by 4 , then $$ \mathrm{a}_{\mathrm{B}}=\frac{2 \mathrm{Vdg}-\mathrm{V} 	imes 4 	imes \mathrm{g}}{\mathrm{~V} 	imes 4} $$ Clearly $\mathrm{a}_{\mathrm{B}}>\mathrm{a}_{\mathrm{A}}$. Here we have neglected the mass of the balloon and considered the mass of the inside gas only\