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The bulk modulus of a spherical object is B. If it is subjected to uniform pressure p, the fractional decrease in radius is (a) p/B (b) B/3p (c) 3p/B (d) p/3B?
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The bulk modulus of a spherical object is B. If it is subjected to uni...
Explanation:
The bulk modulus can be defined as the ratio of the change in pressure to the fractional change in volume. This can be expressed mathematically as:
B = -V(dP/dV)
where B is the bulk modulus, P is the pressure, V is the volume, and dP/dV is the derivative of pressure with respect to volume.
Now, let us consider a spherical object of radius r and volume V. If the object is subjected to a uniform pressure p, the pressure inside the object will be higher than the pressure outside. This will cause a decrease in the volume of the object, which can be expressed mathematically as:
dV = -(4/3)πr^3(dR/R)
where dV is the change in volume, dR is the change in radius, and R is the original radius of the object.
Substituting this expression in the equation for bulk modulus, we get:
B = -(3V)(dP/dV) / (4πr^3(dR/R))
Rearranging this equation, we get:
(dR/R) = -(4πr^3)(dP/dV) / (3V)(B)
This expression gives us the fractional decrease in radius of the object when subjected to a uniform pressure p.
Answer:
The correct option is (a) p/B. Therefore, the fractional decrease in radius is given by:
(dR/R) = -p/B
The bulk modulus can be defined as the ratio of the change in pressure to the fractional change in volume. This can be expressed mathematically as:
B = -V(dP/dV)
where B is the bulk modulus, P is the pressure, V is the volume, and dP/dV is the derivative of pressure with respect to volume.
Now, let us consider a spherical object of radius r and volume V. If the object is subjected to a uniform pressure p, the pressure inside the object will be higher than the pressure outside. This will cause a decrease in the volume of the object, which can be expressed mathematically as:
dV = -(4/3)πr^3(dR/R)
where dV is the change in volume, dR is the change in radius, and R is the original radius of the object.
Substituting this expression in the equation for bulk modulus, we get:
B = -(3V)(dP/dV) / (4πr^3(dR/R))
Rearranging this equation, we get:
(dR/R) = -(4πr^3)(dP/dV) / (3V)(B)
This expression gives us the fractional decrease in radius of the object when subjected to a uniform pressure p.
Answer:
The correct option is (a) p/B. Therefore, the fractional decrease in radius is given by:
(dR/R) = -p/B
Community Answer
The bulk modulus of a spherical object is B. If it is subjected to uni...
Volume of the sphere; V = 4/3. π.r³
or, dV/dr = 3.(4/3).π.r²
or, dV/dr = 4.π.r²
dV can be written as ΔV and dr as Δr
∴ ΔV = 4.π.r².Δr
or, ΔV/V =v. (4.π.r².Δr)/(4/3.π.r³)
or, ΔV/V =v. 3.Δr/r
Now. , Bulk modulus. ; B = -P/(ΔV/V)
or, B. = -P/(3.Δr/r)
or, -Δr/r = P/3B
The final answer will be P/3B.
or, dV/dr = 3.(4/3).π.r²
or, dV/dr = 4.π.r²
dV can be written as ΔV and dr as Δr
∴ ΔV = 4.π.r².Δr
or, ΔV/V =v. (4.π.r².Δr)/(4/3.π.r³)
or, ΔV/V =v. 3.Δr/r
Now. , Bulk modulus. ; B = -P/(ΔV/V)
or, B. = -P/(3.Δr/r)
or, -Δr/r = P/3B
The final answer will be P/3B.
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The bulk modulus of a spherical object is B. If it is subjected to uniform pressure p, the fractional decrease in radius is (a) p/B (b) B/3p (c) 3p/B (d) p/3B?
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The bulk modulus of a spherical object is B. If it is subjected to uniform pressure p, the fractional decrease in radius is (a) p/B (b) B/3p (c) 3p/B (d) p/3B? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The bulk modulus of a spherical object is B. If it is subjected to uniform pressure p, the fractional decrease in radius is (a) p/B (b) B/3p (c) 3p/B (d) p/3B? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The bulk modulus of a spherical object is B. If it is subjected to uniform pressure p, the fractional decrease in radius is (a) p/B (b) B/3p (c) 3p/B (d) p/3B?.
The bulk modulus of a spherical object is B. If it is subjected to uniform pressure p, the fractional decrease in radius is (a) p/B (b) B/3p (c) 3p/B (d) p/3B? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The bulk modulus of a spherical object is B. If it is subjected to uniform pressure p, the fractional decrease in radius is (a) p/B (b) B/3p (c) 3p/B (d) p/3B? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The bulk modulus of a spherical object is B. If it is subjected to uniform pressure p, the fractional decrease in radius is (a) p/B (b) B/3p (c) 3p/B (d) p/3B?.
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