JEE MAIN - Physics (2021 - 31st August Morning Shift - No. 19)
When a rubber ball is taken to a depth of __________m in deep sea, its volume decreases by 0.5%.
(The bulk modulus of rubber = 9.8 $$\times$$ 108 Nm$$-$$2, Density of sea water = 103 kgm$$-$$3, g = 9.8 m/s2)
(The bulk modulus of rubber = 9.8 $$\times$$ 108 Nm$$-$$2, Density of sea water = 103 kgm$$-$$3, g = 9.8 m/s2)
Answer
500
Explanation
$$B = - {{\Delta P} \over {\left( {{{\Delta V} \over V}} \right)}} = - {{\rho gh} \over {\left( {{{\Delta V} \over V}} \right)}}$$
$$ - {{B{{\Delta V} \over V}} \over {\rho g}} = h$$
$${{9.8 \times {{10}^8} \times 0.5} \over {100 \times {{10}^3} \times 9.8}} = h$$
h = 500
$$ - {{B{{\Delta V} \over V}} \over {\rho g}} = h$$
$${{9.8 \times {{10}^8} \times 0.5} \over {100 \times {{10}^3} \times 9.8}} = h$$
h = 500
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