The increase in the pressure required to decrease the volume (ΔV) of water is 6.3 x 10^7 N/m^2. The percentage decrease in the volume is _______. (Bulk modulus of water = 2.1 x 10^9 N/m^2)

The correct answer is Option 2. Full mathematical solution steps and hints are accessible in the interactive StemCET workspace.

Physics Q27 – JEE-MAIN 2026

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Home Physics Mechanical Properties of SolidsQuestion #282

The increase in the pressure required to decrease the volume (

Δ V

) of water is

6.3 \times 10^{7} {N/m}^{2}

. The percentage decrease in the volume is _______. (Bulk modulus of water =

2.1 \times 10^{9} {N/m}^{2}

)

Clue 1 of 3: Understanding Bulk Modulus

The bulk modulus quantifies a substance's resistance to compression under pressure. It relates the change in pressure to the fractional change in volume.

🧠 Full Solution Path

Step 1: Identify the Relevant Formula✦ Active

The bulk modulus ( $B$ ) is defined as the ratio of the change in pressure ( $Δ P$ ) to the fractional change in volume ( $\frac{Δ V}{V}$ ). The formula is given by:

B = - \frac{Δ P}{Δ V / V}

Since we are looking for the percentage decrease in volume, we consider the magnitude of the fractional change:

\frac{| Δ V |}{V} = \frac{Δ P}{B}

Step 2: Calculate the Fractional Decrease in Volume○ Expand

Given values are $Δ P = 6.3 \times 10^{7} {N/m}^{2}$ and $B = 2.1 \times 10^{9} {N/m}^{2}$ . Substitute these into the formula:

\frac{| Δ V |}{V} = \frac{6.3 \times 10^{7} {N/m}^{2}}{2.1 \times 10^{9} {N/m}^{2}}

Perform the calculation:

\frac{| Δ V |}{V} = \frac{6.3}{2.1} \times 10^{7 - 9} = 3 \times 10^{- 2} = 0.03

💡 Teacher's Secret Hint

Ensure units cancel out correctly, leaving a dimensionless fractional change.

Step 3: Convert to Percentage Decrease○ Expand

To express the fractional decrease as a percentage, multiply by $100 %$ :

Percentage decrease = \frac{| Δ V |}{V} \times 100 % = 0.03 \times 100 % = 3 %

Thus, the percentage decrease in volume is $3 %$ , which corresponds to option 2.

💡 Teacher's Secret Hint

Remember to multiply by 100 to convert a fraction to a percentage.

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Physics Question 27 – JEE-MAIN 2026

Clue 1 of 3: Understanding Bulk Modulus

🧠 Full Solution Path