Water flowing from a sphere

Calculus Level 5

A hollow sphere of mass mm and radius 11 metre is placed with it's centre at origin in xyzxyz-space. It is filled completely with water of mass mm. So, now the total mass of system is 2m2m.

A small hole is made at t=0t=0 at the bottom and water starts flowing out of the sphere with a constant volume flow rate.

If the maximum distance of centre of mass of the system from origin during the time t=0t=0 to the time water completely flows out from the sphere is a1nb1n{a}^{\frac{1}{n}}-{b}^{\frac{1}{n}} meters, then what is the value of a+b+n?a+b+n?

Details and assumptions

  • a,b,na,b,n are distinct integers such that 0<a,b,n<200<a,b,n<20.

  • While calculating centre of mass of the system don't consider the water that flown out from the sphere. Only consider the water that is present inside the sphere.

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