Question

A wooden block of volume\[1000c{m^3}\]is suspended from a spring balance. Its weight in air is \[12N\]F. It is suspended in water such that half of the block is below the surface of water. The reading of spring balance is:
(A) \[10N\]
(B) \[9N\]
(C ) \[8N\]
(D) \[7N\]

Answer 1

Hint:In the question it is given that only half of the object is immersed in the water, therefore, only half of the total volume must be considered.

Using this volume, we need to find the buoyant force exerted. This force subtracted from the total weight equals to the weight of the body recorded by the spring balance.

Complete Step By Step Solution:
Volume of the wooden block is given \[ = 1000c{m^3}\]
In the question, it is mentioned that only half of the block is below the surface of the water, this means, that volume of the block inside the water \[ = \dfrac{1}{2} \times 1000c{m^3} = 500c{m^3}\]
We know when the volume of an object is inside any liquid, it displaces a certain mass of liquid ( in this case water) , this mass can be calculated as a product of volume of body immersed and density of the liquid.

\[M = \rho \times V\]

Where,
\[M = \] Mass of water displaced
\[\rho = \] Density of water
\[V = \]Volume of the body
We know density of water is \[1gm/cc\]
Now, putting the values:

\[M = (1 \times 500)gm\]

Now the buoyant force applied by the water on the object \[ = M \times g\]
\[g = \]Acceleration due to gravity

\[g = 10m/{s^2}\]

Buoyant force \[ = 0.5 \times 10N\]
Thus, \[F = 5N\]
Now, the weight measured by the spring balance \[ = (12 - 5)N = 7N\]
This is the required solution.

Therefore, option (D) is correct.

Note:Buoyancy is also responsible for sinking or floating of a body.
When an object floats it is said to have positive buoyancy, as the buoyant force is more than the weight of the body.
When an object sinks it is said to have negative buoyancy, as the weight of the body is greater than the buoyant force.
Buoyancy can also be neutral.