Advertisements
Advertisements
Question
To what depth must a rubber ball be taken in deep sea so that its volume is decreased by 0.1%. (The bulk modulus of rubber is 9.8 × 108 Nm–2; and the density of sea water is 103 kg m–3.)
Solution
Given the Bulk modulus of rubber (K) = 9.8 × 108 N/m2
The density of seawater (ρ) = 103 kg/m3
Percentage decrease in volume, `((ΔV)/V xx 100)` = 0.1
⇒ `(ΔV)/V = 0.1/100`
⇒ `(ΔV)/V = 1/1000`
Let the rubber ball be taken up to depth h.
∴ Change in pressure (p) = hpg
∴ Bulk modulus `(K) = |p/((ΔV)/V)| = (hpg)/(((ΔV)/V))`
⇒ `h = (K xx ((ΔV)/V))/(pg)`
= `(9.8 xx 10^8xx 1/1000)/(10^3 xx 9.8)`
= 100 m
APPEARS IN
RELATED QUESTIONS
Compute the bulk modulus of water from the following data: Initial volume = 100.0 litre, Pressure increase = 100.0 atm (1 atm = 1.013 × 105 Pa), Final volume = 100.5 litre. Compare the bulk modulus of water with that of air (at constant temperature). Explain in simple terms why the ratio is so large.
What is the density of water at a depth where the pressure is 80.0 atm, given that its density at the surface is 1.03 × 103 kg m–3?
Compute the fractional change in volume of a glass slab, when subjected to a hydraulic pressure of 10 atm.
How much should the pressure on a litre of water be changed to compress it by 0.10%?
The Marina trench is located in the Pacific Ocean, and at one place it is nearly eleven km beneath the surface of the water. The water pressure at the bottom of the trench is about 1.1 × 108 Pa. A steel ball of initial volume 0.32 m3 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?
Find the increase in pressure required to decrease the volume of a water sample by 0.01%. Bulk modulus of water = 2.1 × 109 N m−2.
Estimate the change in the density of water in ocean at a depth of 400 m below the surface. The density of water at the surface = 1030 kg m−3 and the bulk modulus of water = 2 × 109 N m−2.
Bulk modulus of a perfectly rigid body is ______.
The bulk modulus of a liquid is 3 × 1010 Nm-2. The pressure required to reduce the volume of liquid by 2% is ______.
The normal density of a material is ρ and its bulk modulus of elasticity is K. The magnitude of the increase in density of the material, when a pressure P is applied uniformly on all sides, will be ______.
