question_answer

A cube of iron whose sides are of length L, is put into mercury. The weight of iron cube is W. The density of iron is pp that of mercury is\[{{\rho }_{M}}\]. The depth to which the cube sinks is given by the expression -

A) \[W{{L}^{2}}{{\rho }_{I}}\]

B)                    \[W{{L}^{2}}{{\rho }_{M}}\]

C)                    \[\frac{W}{{{L}^{2}}{{\rho }_{I}}}\]

D)                    \[\frac{W}{{{L}^{2}}{{\rho }_{M}}g}\]

Correct Answer: D

Solution :

\[W\text{ }=\text{ }upthrust\] \[W\,\,=\,\,({{L}^{2}}x)({{\rho }_{m}})g\] \[x\,\,=\,\,\frac{W}{{{L}^{2}}{{\rho }_{m}}g}\]