A spherical ball contracts in volume by 0.01% when subjected to a norm...
A spherical ball contracts in volume by 0.01% when subjected to a norm...
Introduction:
The problem states that a spherical ball contracts in volume by 0.01% when subjected to a normal uniform pressure of 100 atm. We need to determine the bulk modulus of the material.
Understanding the Problem:
To solve this problem, we need to understand the concept of bulk modulus. The bulk modulus of a material measures its resistance to change in volume under an applied pressure. It is defined as the ratio of the change in pressure to the fractional change in volume.
Formula:
The formula for bulk modulus is given as:
Bulk modulus (K) = -V * ΔP / ΔV
Where:
K = Bulk modulus
V = Initial volume of the material
ΔP = Change in pressure
ΔV = Change in volume
Calculation:
Given:
ΔP = 100 atm (uniform pressure)
ΔV = -0.01% (negative sign indicates contraction)
To find the bulk modulus, we need to determine the initial volume (V). Unfortunately, the problem does not provide a specific value for the initial volume. Therefore, we cannot calculate the exact bulk modulus. However, we can still provide a general explanation of the concept.
Explanation:
The bulk modulus of a material indicates its resistance to volume change under pressure. In this case, the spherical ball contracts in volume by 0.01% when subjected to a normal uniform pressure of 100 atm. This means that the ball's volume decreases by 0.01% of its initial volume.
If we assume the initial volume of the ball is V, then the change in volume (ΔV) can be calculated as:
ΔV = (0.01/100) * V = 0.0001 * V
Substituting the given values into the formula for bulk modulus:
Bulk modulus (K) = -V * ΔP / ΔV
= -V * 100 atm / (0.0001 * V)
= -10000 atm
Conclusion:
Based on the given information, the bulk modulus of the material is -10000 atm. It is important to note that the negative sign indicates the contraction of volume under pressure. However, since the problem does not provide the initial volume, we cannot determine the exact bulk modulus.
To make sure you are not studying endlessly, EduRev has designed NEET study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in NEET.