Mechanical Properties of Solids

JEE Main level, numerical answer, medium

96 of 118

Question 96 of 118

When a rubber ball is taken to a depth of _______ mm in deep sea, its volume decreases by 0.50.5%
(The bulk modulus of rubber =9.8×108Nm−2=9.8\times {10}^{8}N{m}^{-2} Density of sea water =103kgm−3={10}^{3}kg{m}^{-3},g=9.8ms−2g=9.8m{s}^{-2})

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Answer: 500

−dVV=0.5100=0.005\dfrac{-dV}{V}=\dfrac{0.5}{100}=0.005
B=−dPdVV=ρgh−dVVB=\dfrac{-dP}{\dfrac{dV}{V}}=\dfrac{\rho gh}{\dfrac{-dV}{V}}
9.8×108=103×9.8×h5×10−3⇒h=500m9.8\times {10}^{8}=\dfrac{{10}^{3}\times 9.8\times h}{5\times {10}^{-3}}\Rightarrow h=500m

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