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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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w₁ > w₂

w₁ = w₂

w₁ < w₂

cannot be determined

answer is C.

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Detailed Solution

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

W_o-W₁ = V_o D_og and W_o-W₂=V_t D_og.

W₁-W₂ = (V_tD_t-V_oD_o)g

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

$V_{0} D_{0} [(1 + γ_{s} t) {(1 - γ_{l} t)}^{- 1} - 1] g a p p r o x i m a t e l y$

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

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

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