Hello Everyone,
I am trying to solve this difficult problem :
"A heavy spherical ball is lowered carefully into a full conical wine
glass whose depth is h and whose generating angle (between the axis
and a generator) is α. Show that the greatest overflow occurs when
the radius of the ball is sin(α)+cos(2α)h sin(α)".
Work:
1- If the ball is fully immersed, I got
Radius of the ball =1+sin(α)h sin(α)
2- The ball may be too large to be fully immersed and
yet displace more liquid than a smaller ball that is fully immersed.
How to find it in this case ?
Any ideas ? Thanks
I am trying to solve this difficult problem :
"A heavy spherical ball is lowered carefully into a full conical wine
glass whose depth is h and whose generating angle (between the axis
and a generator) is α. Show that the greatest overflow occurs when
the radius of the ball is sin(α)+cos(2α)h sin(α)".
Work:
1- If the ball is fully immersed, I got
Radius of the ball =1+sin(α)h sin(α)
2- The ball may be too large to be fully immersed and
yet displace more liquid than a smaller ball that is fully immersed.
How to find it in this case ?
Any ideas ? Thanks
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