a mass of 3 kg is placed on the massless pistonof area 10 cm2 of a cylindrical vessel containing a gas. find the fractional change in surface of its bulk modulus is 2×10^4N/m2 and placed in the given vessel
Answers
Answer:
Explanation:pressure, P = weight of object placed on piston/base area
= m × g/A
here, m = 3Kg, g = 10m/s²
and A = 10cm² = 10 × 10^-4 m² = 10^-3 m²
P = 3 kg × 10 m/s²/(10^-3 m²)
= 3 × 10⁴ N/m²
now, Bulk modulus = P/(∆V/V)
given, bulk modulus = 2 × 10⁴ N/m²
so, 2 × 10⁴ = 3 × 10⁴/(∆V/V)
or, ∆V/V = 3/2........(1)
now, volume of sphere, V = 4/3 πr³
differentiating with respect to r,
dV = 4πr² dr
or, dV/V = (4πr²)dr/(4/3 πr³)
or, dV/V = 3 dr/r
or, ∆V/V = 3 ∆r/r .....(2)
similarly, surface area of sphere, A = 4πr²
after differentiating with respect to r,
or, dA = 8πr dr
or, dA/A = 2 dr/r
or, ∆A/A = 2 ∆r/r ......(3)
from equations (2) and (3),
∆A/A = (2/3) ∆V/V
from equations (1),
∆A/A = (2/3) × (3/2) = 1
hence, change in surface area = 1
Answer:
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