An aluminium plate foxed in a horizontal position has a hole of diameter 2.000 cm. A steel sphere of diameter 2.005 cm rests on this hole. All the lengths refer to a temperature of 10 degree celsius. The temperature of the entire system is slowly increased. At what temperature will the ball fall down? Coefficient of aluminium is 23x10^-6/degree celsius and that of steel is 11x10^-6/degree celsius.

Dear Cathy,

It will pass through the hole when the diameter of both of them are same.

Let  it happens at temperature t degree.

For steel, V=Vi(1+Υt)

Vi=initial vol

Y=coeff of vol expansion.

For Al A=Ai(1+βt)

Ai=initial area.

we have considered the vol of steel ball but the area of the Al plate as it's a 2D body.

again at the required temperature radii will be the same. hence putting v=4/3∏(r)^3 & A=∏(r)^2 we get

t=218.8 degree

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Soumyajit Das IIT Kharagpur