Question

# The pressure of a vessel is directly proportional to the cube of its volume. If the pressure of the vessel is 125 Bar when the volume of the vessel is 5 Litres.Find the pressure when the volume of the vessel is 2 Litres.

A
8 Bar
B
5 Bar
C
16 Bar
D
22 Bar

Solution

## The correct option is A 8 BarGiven, the pressure (P) of a vessel is directly proportional to the cube of its volume (V). ⇒P∝ V3  Let the constant of variation be k. ⇒P=kV3 Given, at P = 125 Bar, V = 5 Litres. So, k=PV3 =12553=125125=1 ⇒P=V3 Hence, the pressure (P) when the volume of the vessel is 2 Litres = V3=(23)=8 Bar.Mathematics

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