Question

An iceberg is floating in the sea. Out of $10$ parts of its mass, how many will remain above the surface of the water?

• A. Three parts
• B. Two parts
• C. One part
• D. Five parts

Answer 1

The correct option is C One part

Let the mass & volume of iceberg be $M_i$ and $V_i$

Their mass density $=\frac{M}{V}=P_i=0.417g/c{m}^3$

Let the volume below the surface of water be $V_w.$ This

is the volume of water displaced and the buoyant force is

equal to the weight of that displaced water, which has mass

$M_w=V_w{P}_w$ Given $P_w=1$

The iceberg has weight $W_i=M_{i}g$

The buoyant force is equal to the displaced water,

$W_w=M_{w}g$

Since the iceberg is floating, its weight exactly balances

the buoyant force.

$W_w=W_i\Rightarrow M_{w}g=M_{i}g\Rightarrow V_w=\frac{P_i}{P_w}{V}_i$

$\Rightarrow V_w=0.917V_i$

$\Rightarrow$ Almost 90% of an iceberg's volume and mass is under water

Thus 10 % $({10}^{th}$ part) remains above the surface.