A bottle has an opening of radius a and lengt | vedclass

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

Question

(D) The change in volume of the cork is $\Delta V = V_{initial} - V_{final} = \pi (a + \Delta a)^2 b - \pi a^2 b \approx \pi (a^2 + 2a \Delta a) b - \

Vedclass · Accepted Answer

$(4\pi \mu Bb) \Delta a$

Vedclass · Answer

(D) The change in volume of the cork is $\Delta V = V_{initial} - V_{final} = \pi (a + \Delta a)^2 b - \pi a^2 b \approx \pi (a^2 + 2a \Delta a) b - \pi a^2 b = 2\pi a b \Delta a$.The volumetric strain is $\frac{\Delta V}{V} = \frac{2\pi a b \Delta a}{\pi a^2 b} = \frac{2 \Delta a}{a}$.The pressure $P$ exerted by the cork on the walls of the bottle is given by $P = B 	imes 	ext{volumetric strain} = B \left( \frac{2 \Delta a}{a} ight)$.The normal force $N$ exerted by the cork on the inner surface of the bottle opening is $N = P 	imes A_{surface} = \left( \frac{2B \Delta a}{a} ight) 	imes (2\pi a b) = 4\pi B b \Delta a$.The frictional force $f$ required to push the cork is $f = \mu N = \mu (4\pi B b \Delta a) = (4\pi \mu B b) \Delta a$.

Similar Questions

The average depth of an oil well is $2000 \, m$. If the bulk modulus of oil is $8 \times 10^8 \, N/m^2$ and the density of oil is $1500 \, kg/m^3$, the fractional compression at the bottom of the well is (take $g = 10 \, m/s^2$): (in $\%$)

The isothermal bulk modulus of an ideal gas at pressure $P$ is:

The increase in the pressure required to decrease the volume $(\Delta V)$ of water is $6.3 \times 10^7 \text{ N/m}^2$. The percentage decrease in the volume is . . . . . . . (Bulk modulus of water = $2.1 \times 10^9 \text{ N/m}^2$.) (in $\%$)

Calculate the stress developed inside a tooth cavity filled with copper when hot tea at a temperature of $57\,^{\circ}C$ is drunk. You can take the body (tooth) temperature to be $37\,^{\circ}C$ and $\alpha = 1.7 \times 10^{-5}/^{\circ}C$,bulk modulus for copper $= 140 \times 10^9\, N/m^2$.

$A$ solid cube of copper of edge $10 \, cm$ is subjected to a hydraulic pressure of $7 \times 10^6 \, Pa$. If the Bulk modulus of copper is $140 \, GPa$,then the contraction in its volume will be ................ $m^3$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module