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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

w₁ = w₂

c

w₁ < w₂

d

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

= {W_2} > {W_1}\

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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