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The longitudinal waves starting from a ship return from the bottom of the sea to the ship after 2.60 s. If the bulk modulus of water be 220 kg mm−2 and the density is 1.1 × 103 kgm−3,the depth of sea is
(take, g = 9 8.N kg−1)
(a) 1820 m
(b) 1850 m
(c) 1400 m
(d) 1420 m
The longitudinal waves starting from a ship return from the bottom of the sea to the ship after 2.60 s. If the bulk modulus of water be 220 kg mm−2 and the density is 1.1 × 103 kgm−3,the depth of sea is
(take, g = 9 8.N kg−1)
(a) 1820 m
(b) 1850 m
(c) 1400 m
(d) 1420 m
Answer : (a) 1820 m
Given,
K = 220 kg mm-2
= 220\(\times\)106 kgm-2
= 220 \(\times\)9.8 \(\times\)106Nm-2
And,
ρ = 1.1 \(\times\) 103 kgm-3
Velocity,
v = \(\sqrt{\frac{K}{ρ}}\)
= \(\sqrt{\frac{220\times 9.8\times 10^6}{1.1\times 10^3}}\)
= 1400 ms-1
Depth of sea = \(\frac{vt}{2}\)
= \(\frac{1400\times 2.60}{2}\)
= 1820 m.