A block of wood weighs 12 kg and has relative density 0.6. It is immersed in water up to 0.9 of its volume. The weight of a metal needed, if the metal is[RD of metal = 14]a)on the top of wood is 6 kgb)on the top of wood is 12 kgc)attached below the wood is 6.5 kg (approx)d)attached below the wood depends upon the RD of metalCorrect answer is option 'A,C,D'. Can you explain this answer?

Question

Answer

When the metal of mass m1 is on the top of wood of mass M.

ρ and ρw are densities of water and wood, respectively.

When the metal of mass m₂ is attached at the bottom of wood of mass M.

Let VM be the volume of the metal inside the water.

(M + m₂) = (0.9VW + VM)ρ

or,

or, m₂ = 6.5 kg (approx)

Answer

When the metal of mass m1 is on the top of wood of mass M.

ρ and ρw are densities of water and wood, respectively.

When the metal of mass m₂ is attached at the bottom of wood of mass M.

Let VM be the volume of the metal inside the water.

(M + m₂) = (0.9VW + VM)ρ

or,

or, m₂ = 6.5 kg (approx)

Answer

To solve this problem, we need to understand the concept of relative density and the principle of buoyancy.

Relative Density:
Relative density is the ratio of the density of a substance to the density of a reference substance. In this case, the relative density of the wood is given as 0.6. This means that the density of the wood is 0.6 times the density of water.

Buoyancy:
According to Archimedes' principle, an object submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces. This buoyant force helps to determine whether an object will float or sink.

Given information:
Weight of the wood = 12 kg
Relative density of the wood = 0.6
Volume of water displaced by the wood = 0.9 times the volume of the wood

Let's analyze the given options one by one:

a) On the top of wood is 6 kg:
If a metal weighing 6 kg is placed on top of the wood, it will not affect the buoyancy of the wood. The buoyant force acting on the wood will still be equal to the weight of the water displaced by the wood. Hence, this option is correct.

b) On the top of wood is 12 kg:
If a metal weighing 12 kg is placed on top of the wood, it will increase the overall weight of the system. This will cause the wood to sink deeper into the water, displacing more water. As a result, the buoyant force acting on the wood will increase. Therefore, this option is incorrect.

c) Attached below the wood is 6.5 kg (approx):
If a metal weighing 6.5 kg is attached below the wood, it will increase the weight of the wood-metal system. This will cause the system to sink deeper into the water, displacing more water. The buoyant force acting on the system will increase, but it may not be equal to the weight of the water displaced by the system. The exact weight required to achieve this balance would depend on the relative densities of the wood and the metal. Since the relative density of the metal is not given, we cannot determine if this option is correct or not.

d) Attached below the wood depends upon the relative density of the metal:
As explained in option c, the weight required to achieve the balance between the buoyant force and the weight of the system depends on the relative densities of the wood and the metal. Therefore, this option is correct.

In conclusion, options a, c, and d are correct based on the given information.

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