A body with mass $100 k g$ and volume $0.2 m^{3}$ is taken to a depth of 10 meters in water and released. Density of body is less than water. Accelaration of body after it is released is ___.

Accelaration due to gravity $10 m / s^{2}$

Density of water $1000 k g / m^{3}$ )

$10 m / s^{2}$

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$1 m / s^{2}$

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$5 m / s^{2}$

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$4 m / s^{2}$

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Solution

The correct option is A
$10 m / s^{2}$

Given mass $m$ = $100 k g$ , Volume $v$ = $0.2 m^{3}$

Accelaration due to gravity = $10 m / s^{2}$ .

Density of water = $1000 k g / m^{3}$

We know body with less density always floats in a fluid which has more density than the body. After taking it to some depth if it is released freely it will accelerate upwards because buoyant force acting is greater than weight acting in downward direction.

From Newton's second law of motion force $f$ = mass $\times$ accelaration

Net force acting on body is buoyancy in upward direction minus weight in downward direction

Force of buoyancy $b$ = volume of water displaced $\times$ density of water $\times$ accelaration due to gravity

If body is fully immersed volume of water displaced = volume of body

Force of buoyancy $b$ = $0.2 \times 1000 \times 10$ = $2000 N$

Net force $f$ = $b - m g$ = $2000 - 1000$ = $1000 N$

force $f$ = mass $\times$ accelaration

Accelaration = $\frac{1000}{100}$ = $10 m / s^{2}$

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A body with mass 100kg and volume 0.2m3 is taken to a depth of 10 meters in water and released. Density of body is less than water. Accelaration of body after it is released is ___. Accelaration due to gravity 10m/s2 Density of water 1000kg/m3 )

A body with mass $100 k g$ and volume $0.2 m^{3}$ is taken to a depth of 10 meters in water and released. Density of body is less than water. Accelaration of body after it is released is ___.

Accelaration due to gravity $10 m / s^{2}$

Density of water $1000 k g / m^{3}$ )