A cubical block of wood of side a and density ρ floats in water of density $$2$$ρ. The lower surface of the cube just touches the free end of a massless spring of force constant K fixed at the bottom of the vessel. The weight W put over the block so that it is completely immersed in water without wetting the weight is

Question

A cubical block of wood of side a and density ρ floats in water of density $$2$$ρ. The lower surface of the cube just touches the free end of a massless spring of force constant K fixed at the bottom of the vessel. The weight W put over the block so that it is completely immersed in water without wetting the weight is

Infinity Learn · Accepted Answer

Since density of block $$=$$ $$1/2(density$$ of $$water)$$, $$50$$% of its volume is immersed in water.In the second case, half of the volume of the block is further immersed in water. Therefore, $$W=$$ Extra upthrust $$+Spring$$ force $$=a$$×a×$$a2$$×$$2$$ρ×$$g+Ka2=aa2$$ρ$$g+K2$$

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material