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Properties of Matter question

2022 · 24 Jun · Shift 1 · Q44
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  5. /2022 · 24 Jun · Shift 1 · Q44

Properties of Matter question

2022 · 24 Jun · Shift 1 · Q44

JEE MainPhysicsProperties of MatterMCQ+4 / −1
The bulk modulus of a liquid is 3 ×\times× 1010 Nm −-− 2. The pressure required to reduce the volume of liquid by 2% is :
  1. A
    3 ×\times× 108 Nm −-− 2
  2. B
    9 ×\times× 108 Nm −-− 2
  3. C
    6 ×\times× 108 Nm −-− 2
  4. D
    12 ×\times× 108 Nm −-− 2
View written solutionFree

Correct answer: C

  1. Use the definition of bulk modulus

The bulk modulus BBB is given by

B=−ΔPΔV/VB = -\frac{\Delta P}{\Delta V/V}B=−ΔV/VΔP​

For magnitude purposes,

ΔP=B(ΔVV)\Delta P = B \left(\frac{\Delta V}{V}\right)ΔP=B(VΔV​)
  1. Substitute the given values

Given:

B=3×1010 N m−2B = 3 \times 10^{10}\ \text{N m}^{-2}B=3×1010 N m−2

Volume reduction =2%= 2\%=2%, so

ΔVV=2100=0.02\frac{\Delta V}{V} = \frac{2}{100} = 0.02VΔV​=1002​=0.02

Hence,

ΔP=3×1010×0.02\Delta P = 3 \times 10^{10} \times 0.02ΔP=3×1010×0.02
  1. Calculate
0.02=2×10−20.02 = 2 \times 10^{-2}0.02=2×10−2

So,

ΔP=3×1010×2×10−2\Delta P = 3 \times 10^{10} \times 2 \times 10^{-2}ΔP=3×1010×2×10−2 ΔP=6×108 N m−2\Delta P = 6 \times 10^8\ \text{N m}^{-2}ΔP=6×108 N m−2
  1. Match with the options
6×108 N m−26 \times 10^8\ \text{N m}^{-2}6×108 N m−2

This corresponds to Option C.

  1. Comparison with stored answer

Stored correct answer: C

My derived answer: C

So, they agree.

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