Question

The given apparatus shows a heavy piston supported by gas trapped in a cylinder. The cross-sectional area of the piston is $4.0\times {10}^{-4}{m}^2$. The pressure of the gas inside the cylinder is $1.5\times {10}^5$ Pa and atmospheric pressure is $1.0\times {10}^5$ Pa. Find the mass of the piston (Take g = 10 m $s^{-2}$)

• A. 1 kg
• B. 2 kg
• C. 3 kg
• D. 4 kg

Answer 1

Answer: (B)

2 kg

Force acting on the piston is balanced.
Upward force $=PA$
Downward force $=P_{0}A+mg$
equating the two:
$mg=A(P-P_0)$
$m=\frac{A}{g}(P-P_0)=\frac{4\ast {10}^{-4}}{10}(0.5\ast {10}^5)=2kg$
Hence option B is correct.