Don\'t have to find the new radius, just the force as a function of the new radi

Question

Don't have to find the new radius, just the force as a function of the new radius R1.

A perfectly spherical balloon is inflated to a radius of R0 = 11 cm. It has an internal pressure P0 of 110 kPa, with an atmospheric pressure Pa of 100 kPa. The tensile strength (more properly: surface tension) of the balloon, T, is a constant 500 N/m, and is related to the pressures and the radius by T = (P0 - Pa)R0/2. A positive charge of 0.1 mC is sprayed uniformly over the surface of the balloon. What is the pressure (force per unit area) exerted on the face of the balloon by these charges, as a function of the new radius R1? Is this pressure inward or outward?

Explanation / Answer

T = (110-100)*(Ro)/2 = 5*Ro

new radius = R1

let pressure be P1

T = (P1-Pa)*R1/2 = 500 .......(1)

Pa = 100000Pa

P1 = Force/(4*pi*R1^2)

substitute P1 in the eqn. (1)

you get Force as a function of R1

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