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Q.

 A metal ball immersed in alcohol weighs w1 at 00 C and W2  at 500C. The coefficient of cubical expansion of the metal is less than that of alcohol. If the density of the metal is large compared to that of alcohol, then

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a

w1 = w2

b

cannot be determined

c

w1 > w2   

d

w1 < w2

answer is C.

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Detailed Solution

If  W0 is the weight of the metal in air, then

Wo-W1   =    Vo Dog and Wo-W2=Vt Dog.

W1-W2   =   (VtDt-VoDo)g

            

= \left[ {{V_o}\left( {1 + {\gamma _s}t} \right)\,\,{D_o}{{(1 + {\gamma _\ell }t)}^{ - 1}} - {V_o}{D_o}} \right]g

            V0D01+γst1-γlt-1-1g approximately

 

            

= {V_o}{D_o}\left( {{\gamma _s} - {\gamma _\ell })t} \right)

            

= {\gamma _s} < {\gamma _\ell } \Rightarrow {W_1} - {W_2} < 0

            

= {W_2} > {W_1}\

 

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