Question

A rubber ball be taken in a deep sea so that its volume is decreased by \( x %\). The bulk modulus of rubber is \( K \) and density of sea water is \( \rho \). The depth to which a rubber ball is taken is proportional to

• A. \( \frac{Qx}{Kg} \)
• B. \( \frac{Kx}{Qg} \)
• C. \( \frac{gq}{Kx} \)
• D. \( \frac{Q}{Kxg} \)

Hint:

In problems involving bulk modulus, the change in volume is related to the change in pressure. The depth under water can be calculated using the pressure and density of water.

Answer 1

The Correct Option is B

Step 1: Understanding the volume change in the rubber ball.
The change in volume of the rubber ball when taken under water is given by the equation: \[ \Delta V = - \frac{V}{K} \Delta P \] Where \( K \) is the bulk modulus, \( V \) is the volume of the ball, and \( \Delta P \) is the change in pressure. The pressure is related to the depth of water by: \[ \Delta P = \rho g h \] Thus, the depth \( h \) is proportional to the given formula: \[ h = \frac{Kx}{Qg} \] Thus, the correct answer is (B) \( \frac{Kx}{Qg} \).