The Marina trench is located in the Pacific Ocean- and at one place it is nearly 11 - beneath the surface of water- The water pressure at the bottom of the trench is about 1-1 - 108 - A steel ball of initial volume 0-32 -3 is dropped into the ocean and falls to the bottom of the trench- What is the change in the volume of the ball when it reaches to the bottom-

Given, Bulk modulus of steel, (𝐵)=160×10^9 𝑁/𝑚^2 Initial volume of steel Ball, (𝑉)=0.32 m^3 →△ 𝑉=−(𝑉𝐵) Putting values, we get, ⇒=−(0.32 𝑚^3×1.1×10^8 𝑃𝑎160 ...

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Standard IX

History

The Ottoman Empire

The Marina tr...

Question

The Marina trench is located in the Pacific Ocean, and at one place it is nearly $11 k m$ beneath the surface of water. The water pressure at the bottom of the trench is about $1.1 \times 10^{8} P a$ . A steel ball of initial volume $0.32 m^{3}$ is dropped into the ocean and falls to the bottom of the trench. What is the change in the volume of the ball when it reaches to the bottom?

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Solution

Given,
Bulk-modulus of steel, $(B) = 160 \times 10^{9} N / m^{2}$

Initial volume of steel Ball, $(V) = 0.32 m^{3}$

$\to△ V = - (\frac{V △ P}{B})$

Putting values, we get,

$\Rightarrow△ V = - (\frac{0.32 m^{3} \times 1.1 \times 10^{8} P a}{160 \times 10^{9} P a})$

$= - 2.2 \times 10^{- 4} m^{3}$

Negative sign indicates that ball gets
compressed or contracted by $2.2 \times 10^{- 4} m^{3} .$

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TheMarina trench is located in the Pacific Ocean, and at one place it isnearly eleven km beneath the surface of water. The water pressure atthe bottom of the trench is about 1.1 × 10⁸Pa. A steel ball of initial volume 0.32 m³is dropped into the ocean andfalls to the bottom of the trench. What is the change in the volumeof the ball when it reaches to the bottom?

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Given, Bulk-modulus of steel, (B)=160×109 N/m2 Initial volume of steel Ball, (V)=0.32 m3 →△V=−(V△PB) Putting values, we get, ⇒△V=−(0.32m3×1.1×108Pa160×109Pa) =−2.2×10−4 m3 Negative sign indicates that ball gets compressed or contracted by 2.2×10−4 m3.