A) \[\frac{{{l}_{a}}}{{{l}_{w}}}\]
B) \[\frac{{{l}_{a}}}{{{l}_{a}}-{{l}_{w}}}\]
C) \[\frac{{{l}_{w}}}{{{l}_{a}}-{{l}_{w}}}\]
D) \[\frac{{{l}_{w}}}{{{l}_{a}}}\]
Correct Answer: B
Solution :
Case-I (in air) \[Y=\frac{FL}{A\Delta l}=\frac{FL}{A{{l}_{a}}}\therefore {{F}_{Trust}}=v\,\rho g\] \[=\frac{v\,\rho g}{A{{l}_{a}}}\] ?(1) Case - 2 when the lead is immersed in a liquid, \[{{W}_{net}}={{W}_{b}}-Thrust\] \[=V\,\rho g\,-V\times {{\rho }_{w}}\times g\] \[=V\,\rho g\,-V\times 1\times g\] \[=\frac{\left( V\,\rho g\,-V\times 1\times g \right)L}{A{{l}_{w}}}\] ?.(2) Y is same, because material is same (1) = (2) we get \[\rho =\frac{{{l}_{a}}}{{{l}_{a}}-{{l}_{w}}}\]
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