Elasticity | JEE Main previous year questions with Solutions

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Topic Question Set

Q 1 :
If average depth of an ocean is 4000m and the bulk modulus of water is $2 \times 10^{9}$ $N m^{- 2}$ , then fractional compression $\frac{∆ V}{V}$ of water at the bottom of ocean is $α \times 10^{- 2}$ . The value of $α$ is ______ . $(G i v e n, g = 10 m s^{- 2}, ρ = 1000 k g$ $m^{- 3})$ [2024]

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(2) $B = \frac{Δ P}{(\frac{Δ V}{V})}$

$- (\frac{Δ V}{V}) = \frac{ρ g h}{B} = \frac{1000 \times 10 \times 4000}{2 \times 10^{9}}$

$= 2 \times 10^{- 2} [- ve sign represents compression]$

Q 2 :
The depth below the surface of sea to which a rubber ball be taken so as to decrease its volume by 0.02% is ______ m.

$(T a k e d e n s i t y o f s e a w a t e r = 10^{3} k g m^{- 3}, B u l k m o d u l u s o f r u b b e r = 9 \times 10^{8} N m^{- 2}, a n d g = 10 m s^{- 2})$   [2024]

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(18) $β = \frac{- Δ P}{\frac{Δ V}{V}} \Rightarrow Δ P = - β \frac{Δ V}{V}$

$ρ g h = - β \frac{Δ V}{V}$

$10^{3} \times 10 \times h = - 9 \times 10^{8} \times (- \frac{0.02}{100}) \Rightarrow h = 18 m$

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