In the figure, chamber A contains a gas, a mo | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let $M$ be the mass of chamber $B$ and $m$ be the mass of each ball. The total downward force exerted by the chamber and the balls on the gas is $

Vedclass · Accepted Answer

$1/n$

Vedclass · Answer

(D) Let $M$ be the mass of chamber $B$ and $m$ be the mass of each ball. The total downward force exerted by the chamber and the balls on the gas is $F = (M + nm)g$. If $A$ is the cross-sectional area of the chamber, the pressure $P$ of the gas is given by $P = F/A = (M + nm)g / A$. When one ball is removed, the new force is $F^{\prime} = (M + (n-1)m)g$. The new pressure $P^{\prime}$ is $P^{\prime} = F^{\prime} / A = (M + (n-1)m)g / A$. The difference in pressure is $P - P^{\prime} = (M + nm)g/A - (M + nm - m)g/A = mg/A$. Thus, $(P - P^{\prime}) / P = (mg/A) / ((M + nm)g/A) = m / (M + nm)$. Assuming the mass of the chamber $M$ is negligible compared to the total mass of the balls (or that the problem implies the weight is primarily due to the balls), we have $M \approx 0$. Then, $(P - P^{\prime}) / P = m / (nm) = 1/n$.

Similar Questions

Two vessels $A$ and $B$ have the same base area and contain water to the same height,but the mass of water in $A$ is four times that in $B$. The ratio of the liquid thrust at the base of $A$ to that at the base of $B$ is (in $:1$)

Define thrust and pressure and give their unit and dimensional formula.

The densities of ice and water are $\rho$ and $\sigma$ respectively. What is the change in volume when a mass $M$ of ice melts?

In which layer of the atmosphere is water vapour present?

Vedclass Test Series

Exam Paper Generator

Online Exam Module