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# 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}

Last updated date: 20th Jun 2024
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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.

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”.