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A bakelite breaker has volume capacity of  500 \; cc at 30^{o}c when it is partially filled with V_{m} volume (at 30^{o}c ) of mercury, it is found that the unfilled volume of the beaker remains constant as temp is varied. If  y_{(beaker)}=6\times 10^{-6} \ (^{\circ}C)^{-1} and y_{(mercury)}=1.5\times 10^{-4} \ (^{\circ}C)^{-1} , Where y is the cooefficient of volume expansion then V_{m}(in \; cc) is close to -
Option: 1 10
Option: 2 20
Option: 3 30
Option: 4 40

Answers (1)


V_b=V_m+V_R\\ \Rightarrow \Delta V_b=\Delta V_m+\Delta V_R\\ \Rightarrow \gamma_b \times \Delta T_b \times V_b=\gamma_m \times \Delta Tm \times V_m\ \ \ \ \ \ \ \ \ \ [\because \Delta V_R=0]\\ \Rightarrow \left[\frac{\gamma_b}{\gamma_m} \right ]V_b=V_m\\ \Rightarrow V_m=20 cc


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