An open and wide glass tube is immersed verti | vedclass

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

Question

(C) Initially,the air column length $L_i = 0.05 \, m = 5 \, cm$. The pressure of the air $P_i = P_{atm} = 76 \, cm$ of $Hg$.When the tube is raised by

Vedclass · Accepted Answer

$0.1$

Vedclass · Answer

(C) Initially,the air column length $L_i = 0.05 \, m = 5 \, cm$. The pressure of the air $P_i = P_{atm} = 76 \, cm$ of $Hg$.When the tube is raised by $0.43 \, m = 43 \, cm$,let the new length of the air column be $x \, cm$. The mercury level inside the tube rises by $(48 - x) \, cm$ relative to the initial position,where $48 \, cm$ is the total displacement of the tube relative to the mercury surface.The final pressure of the air inside the tube is $P_f = P_{atm} - (48 - x) = 76 - 48 + x = (28 + x) \, cm$ of $Hg$.Since the temperature remains constant,we apply Boyle's Law: $P_i V_i = P_f V_f$.Assuming the cross-sectional area $A$ is constant:$76 	imes 5 	imes A = (28 + x) 	imes x 	imes A$$380 = 28x + x^2$$x^2 + 28x - 380 = 0$Solving the quadratic equation:$x = \frac{-28 \pm \sqrt{28^2 - 4(1)(-380)}}{2} = \frac{-28 \pm \sqrt{784 + 1520}}{2} = \frac{-28 \pm \sqrt{2304}}{2} = \frac{-28 \pm 48}{2}$Taking the positive root: $x = \frac{20}{2} = 10 \, cm = 0.1 \, m$.

Similar Questions

At $100 \, K$ and $0.1 \, \text{atm}$ pressure, the volume of helium gas is $10 \, \text{litres}$. If volume and pressure are doubled, its temperature will change to ....... $K$.

Two vessels separately contain two ideal gases $A$ and $B$ at the same temperature. The pressure of $A$ is twice that of $B.$ Under such conditions,the density of $A$ is found to be $1.5$ times the density of $B.$ The ratio of the molecular weight of $A$ to that of $B$ is

$A$ container $A$ contains a gas at thermodynamic coordinates $P, V,$ and $T$. Another container $B$ contains a different gas at $2P, V/4,$ and $2T$. The ratio of the number of molecules in container $A$ to the number of molecules in container $B$ is:

In the given $(V - T)$ diagram,what is the relation between pressures $P_1$ and $P_2 \,?$

$A$ tyre kept outside in sunlight bursts after some time because of:

Vedclass Test Series

Exam Paper Generator

Online Exam Module