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Area and Volume Expansion

A body of mas...

Question

A body of mass $10 k g$ is floating in water with half of its volume inside. The force required to wholly submerge it into water is

A

10 N

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B

49 N

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C

98 N

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D

O r b i t a r y

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Solution

The correct option is B $49 N$
Let the volume of the boat is V and the volume of water displaced be the boat is $\frac{V}{2}$

So, Mass of water displaced be the boat is,

$= \frac{V}{2} \times d e n s i t y o f b o a t$

$= \frac{V}{2} \times \frac{M}{V}$

$= \frac{M}{2}$

$= \frac{10}{2}$

$= 5 K g (M = 10 K g g i v e n)$

So, the mass displaced by boat is $5 K g$

The force required to wholly submerge it into water is,

$= m g$

$= 5 \times 9.8$

$= 49 N$

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