question_answer

A 700 g solid cube having an edge of length 10 cm floats in water. The volume of cube outside water is:

A)  \[2.4\,c{{m}^{3}}\]  

B)  \[4.8\,c{{m}^{3}}\]

C)  \[300\,c{{m}^{3}}\]

D)  \[500\,c{{m}^{3}}\]

Correct Answer: C

Solution :

 Key Idea: When a solid body is immersed in a liquid, then there is some apparent loss in its weight. Two forces act on the cube: (i) weight (mg) of body (downwards) (ii) upthrust (U) of liquid (upwards). For floatation \[U=mg\] Let V be volume of cube inside liquid, then \[V\times d\times g=mg\] \[V\times 1000\times 10=0.7\times 10\] \[\Rightarrow \] \[V=\frac{7}{10.000}{{m}^{3}}=700\,c{{m}^{3}}\] Total volume of cube \[=\,{{(10\,cm)}^{3}}\] \[=100\,c{{m}^{3}}\] Volume outside water \[=1000-700=300\,c{{m}^{3}}\]