A ball falling in a lake of 200 m shows a decrease of 0.1% in its volume. The bulk modulus of elasticity of the material of the ball is: (take g =10 m/s2)
Correct answer: B. 2 x 10^9 N/m2
- A. 109 N/m2
- B. 2 x 10^9 N/m2
- C. 3 x 10^9 N/m2
- D. 4 x 10^9 N/m2
Explanation
The bulk modulus of elasticity is defined as the ratio of the change in pressure to the fractional change in volume. Here, the pressure change can be calculated as ΔP = ρgh, where ρ is the density of water (1000 kg/m3), g is the acceleration due to gravity (10 m/s2), and h is the depth (200 m). Thus, ΔP = 1000 × 10 × 200 = 2 × 106 N/m2. The volume change is given as 0.1%, or 0.001 in decimal form. Using the formula for bulk modulus, B = ΔP / (ΔV/V), we find B = (2 × 106 N/m2) / 0.001 = 2 × 109 N/m2. Therefore, option B is correct. Options A, C, and D do not match the calculation based on the given parameters.
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