Question

A balloon is filled with helium and let go. It rises into the air accelerating at a rate of 0.151 m s−2.

If the density of air is 1.22 kg m−3 then what is the average density of the balloon? (to 3 s.f and in kg m−3)

(Note: use g = 9.81 m s−2 and ignore any "drag" forces on the balloon such as air resistance.)

Answer 1

$$ma=\rho_a gV-mg$$

$$\rho_b Va=\rho_a gV-\rho_b gV$$

$$\rho_b (a+g)=\rho_a g$$

$$\rho_b (0.151+9.81)=1.22 (9.81)$$

$$\rho_b=1.20\frac{kg}{m^3}$$