Answer:
The tension is [tex]T = 4326.7 \ N[/tex]
Explanation:
From the question we are told that
The total mass is [tex]m = 200 \ kg[/tex]
The radius is [tex]r = 5 \ m[/tex]
The density of air is [tex]\rho_a = 1.225 \ kg/m^3[/tex]
Generally the upward force acting on the balloon is mathematically represented as
[tex]F_N = T + mg[/tex]
=> [tex](\rho_a * V * g ) = T + mg[/tex]
=> [tex]T = (\rho_a * V * g ) - mg[/tex]
Here V is the volume of the spherical helium filled balloon which is mathematically represented as
[tex]V = \frac{4}{3} * \pi r^3[/tex]
=> [tex]V = \frac{4}{3} * 3.142 *(5)^3[/tex]
=> [tex]V = 523.67\ m^3[/tex]
So
[tex]T = (1.225 * 523.67* 9.8 ) - 200 * 9.8[/tex]
[tex]T = 4326.7 \ N[/tex]
