A sphere of radius 3 cm is subjected to a pressure of 100 atm. Its volume decreases by 0.3 c.c. What will be its bulk modulus?
Bulk modulus is a measure of a material’s resistance to uniform compression. It is defined as the ratio of the applied pressure to the resulting relative volume change. A high bulk modulus indicates that the material is stiff and does not easily compress. It is expressed in pascals (Pa).
Chapter 8 of Class 11 Physics explains mechanical properties of solids including stress strain and Hooke’s law. It covers Young’s modulus bulk modulus and shear modulus. The chapter discusses elastic potential energy Poisson’s ratio and the response of materials to external forces. These concepts help in understanding material behavior under different conditions.
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We can use the formula to find the bulk modulus as follows:
Bulk Modulus (B) = (Pressure × ΔV) / V
Where:
– Pressure P = 100 atm
– Change in volume ΔV = 0.3 c.c.
– Initial volume V of the sphere is given by the formula for the volume of a sphere:
V = (4/3) π r³
For r = 3 cm:
V = (4/3) π (3)³ = 36 π c.c.
Now, let’s calculate the bulk modulus:
B = (100 atm × 0.3 c.c.) / (36 π c.c.)
Simplifying the above expression gives us the answer
B = 4 π × 10⁵ atm
Thus the correct answer is
4π x 10⁵ atm
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