JEE MAIN - Physics (2021 - 17th March Evening Shift - No. 18)
An object is located at 2 km beneath the surface of the water. If the fractional compression $${{\Delta V} \over V}$$ is 1.36%, the ratio of hydraulic stress to the corresponding hydraulic strain will be ____________. [Given : density of water is 1000 kgm$$-$$3 and g = 9.8 ms$$-$$2]
1.44 $$\times$$ 107 Nm$$-$$2
1.44 $$\times$$ 109 Nm$$-$$2
1.96 $$\times$$ 107 Nm$$-$$2
2.26 $$\times$$ 109 Nm$$-$$2
Explanation
$$\beta = {{\Delta p} \over {{{\Delta V} \over V}}}$$
$$ \Rightarrow $$ $$\beta = {{\Delta \rho gh} \over {{{\Delta V} \over V}}} = {{1000 \times 9.8 \times 2 \times {{10}^3}} \over {{{1.36} \over {100}}}}$$
$$ \Rightarrow $$ $$\beta$$ = 1.44 $$\times$$ 109 N/m2
$$ \Rightarrow $$ $$\beta = {{\Delta \rho gh} \over {{{\Delta V} \over V}}} = {{1000 \times 9.8 \times 2 \times {{10}^3}} \over {{{1.36} \over {100}}}}$$
$$ \Rightarrow $$ $$\beta$$ = 1.44 $$\times$$ 109 N/m2
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