Properties Of Solids And Liquids Question 558
Question: A wooden cylinder of 50 kg is floating in water. A weight of 2 kg is to be placed on it to just make it submerge when the temperature is $ 10{}^\circ C $ . How much less weight is to be placed when temperature increases to $ 30{}^\circ C $ ? (Given $ {\gamma _{water}}={{10}^{-4}}{{/}^{o}}C,{\gamma _{wood}} $ is negligible.):
Options:
A) 104 g
B) 58 g
C) 208 g
D) 54 g
Show Answer
Answer:
Correct Answer: A
Solution:
$ mg+Mg={\rho _{\omega }}Vg $
$ m’g+Mg=\frac{{\rho _{\omega }}}{1+\gamma \Delta T}Vg $
$ m-m’=\rho ( \omega -\frac{{\rho _{\omega }}}{1+\gamma \Delta T} )g( \frac{{\rho _{\omega }}\gamma \Delta T}{1+\gamma \Delta T} )V _{g} $
$ 52g={\rho _{\omega }}Vg $
$ 2-m’\approx \frac{52\times {{10}^{-4}}\times 20}{1}=104gm. $
