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An object is located at 2 km beneath the surface of the water. If the fractional compression (Δ V)/V is 1.36%, the ratio of hydraulic stress to the corresponding hydraulic strain will be ______. (Given : Density of water is 1000 kg m⁻³ and g=9.8 m s⁻².)

Asked in JEE Main 17th March 2nd Shift 2021 · Bulk modulus and compressibility

• (1) 1.44×10⁹ N m⁻²
• (2) 2.26×10⁹ N m⁻²
• (3) 1.44×10⁷ N m⁻²
• (4) 1.96×10⁷ N m⁻²

Step-by-step solution

Why the other options are wrong

• (2) comes from no consistent slip lands here; it is a filler distractor. To reach 2.26×10⁹ the strain would have to be 0.867%, which is not 1.36% nor any simple mangling of it.
• (3) comes from carries the right digits with the wrong power of ten: it comes from dividing by 1.36 instead of by 0.0136, i.e. treating the percentage as though it were already a fraction.
• (4) comes from is the hydraulic stress ρ gh=1.96×10⁷ N m⁻² on its own, stopping before the division by the strain that the question actually asks for.

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