Question

When a polar bear jumps on to an ice-berg, its weight 200kg wt. is just sufficient to sink the iceberg. Then the weight of iceberg is (specific gravity of ice=0.9; specific gravity of seawater=1.02):
$\begin{align}
  & (A)1500kg.wt \\
 & (B)1000kg.wt \\
 & (C)3000kg.wt \\
 & (D)2040kg.wt \\
\end{align}$

Answer 1

Hint:Here we want to find the weight of the ice-berg. For this assume that the upward force and downward forces are equal here. For this first calculate the upward force and then calculate the downward force. On equating the both equations and solving them, we will get the weight of the ice- berg.

Complete answer:
 Let the weight of iceberg be $M$ and weight of iceberg is 200kgwt.
We know that,
Density, $\rho =\dfrac{M}{V}$
Then its volume is,
$V=\dfrac{M}{\rho }$
Here Density, $\rho =$ Specific gravity$\times {{10}^{3}}kg/{{m}^{3}}$
Thus by substituting the value of $\rho $ we get,
$\Rightarrow V=\left( \dfrac{M}{0.9\times {{10}^{3}}} \right)$
Hence the weight of displaced water$=(V\times 1.02\times {{10}^{3}})$$N$
Net upward force, ${{F}_{upward}}=Mg+200g$
Net downward force, ${{F}_{downward}}=V\rho g=\left( \dfrac{M}{0.9\times {{10}^{3}}} \right)\times \left( 1.02\times {{10}^{3}} \right)\times g$
Here, the net upward force and downward forces are equal.
Hence by equating them we get,
$Mg+200g=\left( \dfrac{M}{0.9\times {{10}^{3}}} \right)\times \left( 1.02\times {{10}^{3}} \right)\times g$
$\Rightarrow (M+200)\times g=\left( \dfrac{M}{0.9\times {{10}^{3}}} \right)\times (1.02\times {{10}^{3}})\times g$
Here both left hand side and right hand side contain $g$ .
Hence cancelling them equation becomes,
$\Rightarrow (M+200)=\left( \dfrac{M}{0.9\times {{10}^{3}}} \right)\times (1.02\times {{10}^{3}})$
$\Rightarrow \left( M+200 \right)=\left( 1.133M \right)$
Taking the terms that containing $M$ in right hand side and other terms in left hand side we get,
$\Rightarrow 200=1.133M-M$
Thus equation becomes,
$\Rightarrow 200=0.133M$
Therefore,
$\Rightarrow M=1500kgwt$
The weight of the iceberg is 1500kgwt.

So, the correct answer is “Option A”.

Additional Information:
Buoyant force is an example of upward force. The material which has less density always flows on water. At that time buoyancy force will be equal to force of gravity.

Note:
The force that exerts on the surface of the object is called the normal force. For an object at rest, the net force on that object will be equal to zero. In that case the upward force and the downward force will be equal. Here, the downward force is the weight exerted by the object and upward force is the normal force.