A balloon filled with gas evenly lifts up a load of mass m. Air density p, ball mass M.

A balloon filled with gas evenly lifts up a load of mass m. Air density p, ball mass M. What is the volume of the ball?

Given:

M is the mass of the balloon;

m is the mass of the load that lifts the balloon;

g is the acceleration of gravity;

ro is the density of the air.

It is required to determine the volume of the ball V.

Since the condition of the problem is not specified, the air resistance is not taken into account. Then, uniform movement is possible when the action of all forces is balanced. Since 2 forces act on the ball: gravity and Archimedean force, then:

F gravity = Farkhimedov;

(m + M) * g = ro * V * g;

m + M = ro * V;

V = (m + M) / ro.

Answer: the volume of the balloon is (m + M) / ro.