A) \[\frac{1+100\gamma t}{1+\gamma t}\]
B) \[\frac{1+\gamma t}{1+100\,\gamma t}\]
C) \[\frac{100+\gamma t}{1+\gamma t}\]
D) \[\frac{1+\gamma t}{100+\gamma t}\]
Correct Answer: A
Solution :
Let \[\rho {{}_{1}}\]is the density of liquid at\[t{{\,}^{o}}C\] and \[\gamma \] is the coefficient of expansion. Then, \[p{{}_{2}}={{\rho }_{1}}(1-\gamma t)\] ?(i) Similarly, if \[\rho {{}_{2}}\]is the density of cork having coefficient of expansion \[100\gamma \] at \[t{{\,}^{o}}C\] Then \[\rho {{}_{2}}={{\rho }_{2}}(1-\gamma t)={{\rho }_{2}}(1-100\gamma \,t)\] ?(ii) the cork will sink k at \[t{{\,}^{o}}C\] if \[\rho {{}_{1}}=\rho {{}_{2}}\] or \[\frac{\rho {{}_{1}}}{\rho {{}_{2}}}=1\] ?(iii) Now, putting the values from Eqs. (i) and (ii) in Eq. (iii), we obtain \[\frac{{{\rho }_{1}}(1-\gamma t)}{{{\rho }_{2}}(1-100\gamma t)}=1\] \[\frac{{{\rho }_{2}}}{{{\rho }_{1}}}=\frac{1-\gamma t}{1-100\gamma t}\] or \[\frac{{{\rho }_{2}}}{{{\rho }_{1}}}=\frac{{{(1-100\gamma t)}^{-1}}}{{{(1-\gamma t)}^{-1}}}\] \[\frac{{{\rho }_{2}}}{{{\rho }_{1}}}=\frac{1+100\gamma t}{(1+\gamma t)}\] (using Binomial theorem)
You need to login to perform this action.
You will be redirected in
3 sec
