Question

A block of wood weighs 12kg and has a relative density 0.6. It is to be in water with 0.9 of its volume immersed. The weight of a metal which is needed (a) if the metal is on the top of wood. (b)if the metal is attached below the wood is [Relative density of metal $=$14]:

• A. 6kg, 7.5 kg
• B. 6kg, 6.5 kg
• C. 6.5 kg, 7.5 kg
• D. 7 kg, 8.5 kg

Answer 1

The correct option is B 6kg, 6.5 kg

a) let the weight of metal needed be m

volume of metal $=m/14$

Weight of wood $=12kg$

volume of wood $=12/0.6=20$

Total volume $=20+m/14$

Now, Weight $=$ buoyant force

The volume displaced will be of only of wood:

=> $(m+12)g=g(0.9\times 20)$

=> m = 6 Kg

b) Now, Weight = buoyant force

The volume displaced will be of wood and metal:

$(m+12)g=(0.9\times 20+\frac{m}{14})g$

=> $m=6.46Kg=6.5$ Kg (approximately)

Answer. B