Calculating Resistance Across a Hollow Sphere

AI Thread Summary
To calculate the resistance of a hollow sphere with internal radius R1 and outer radius R2, the relevant formula is R = ρ * l / A, where ρ is resistivity, l is the thickness (R2 - R1), and A is the cross-sectional area. The resistance is determined by considering the area of the inner and outer surfaces and treating the hollow sphere as a series of thin shells. The approach involves integrating the resistance contributions from each shell to find the total resistance from the inner to the outer surface. This method simplifies the problem by using the properties of a trapezoid for the cross-sectional areas. Understanding these concepts is essential for solving the problem effectively.
raj01b
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Homework Statement


What is the resistance of a hollow sphere made of a material having resistivity p. Its internal radius is R1 & outer radius is R2 ?



Homework Equations


R=rho*l/A



The Attempt at a Solution


Here rho=p, l= R2-R1
have no clue, how to attempt the question.
 
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welcome to pf!

welcome to pf!

(have a rho: ρ and try using the X2 icon just above the Reply box :wink:)

the question is asking for the resistance from the inner surface to the outer surface

find the area of the two surfaces, then treat it the same way as a trapezoid with the same top and bottom areas …

what do you get? :smile:​
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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