IAT (IISER) 2026 | Elasticity Question 1 | Physics

An exotic spherical jellyfish has a bulk modulus $B$. Close to the surface of the sea (depth $d=0$), its radius is $R$. When it dives to a depth $d$ ($d \gg R$), its radius is reduced by $\Delta R > 0$. Given the density of the incompressible sea water $\rho$, and the uniform acceleration due to gravity $g$ such that $\rho g d \ll B$, what is $\dfrac{\Delta R}{R}$?

$\left[1 - \left(1 - \dfrac{\rho g d}{B}\right)^{2/3}\right]$

$\left[1 - \left(1 - \dfrac{\rho g d}{B}\right)^{1/3}\right]$

$\left[\left(1 + \dfrac{\rho g d}{B}\right)^{1/3} - 1\right]$

$\left[\left(1 + \dfrac{\rho g d}{B}\right)^{2/3} - 1\right]$

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