Properties of Solids & Fluids · JEE Main previous year questions

Same gas is filled in two vessels of the same volume at the same temperature. If the ratio of the number of molecules is $1:4$, then A. The r.m.s. velocity of gas molecules in two vessels will be the same. B. The ratio of pressure in these vessels will be $1:4$. C. The ratio of pressure will be $1:1$. D. The r.m.s. velocity of gas molecules in two vessels will be in the ratio of $1:4$. Choose the correct answer from the options given below :

1. A.A and C only
2. B.B and D only
3. C.A and B only
4. D.C and D only

A steel wire of length $3.2\mathrm{m}$ $\left({\mathrm{Y}}_{\mathrm{s}}=2.0\times 10^{11}\mathrm{N}{\mathrm{m}}^{-2}\right)$ and a copper wire of length $4.4\mathrm{m}$ $\left({\mathrm{Y}}_{\mathrm{c}}=1.1\times 10^{11}\mathrm{N}{\mathrm{m}}^{-2}\right)$, both of radius $1.4\mathrm{mm}$ are connected end to end. When stretched by a load, the net elongation is found to be $1.4\mathrm{mm}$. The load applied, in Newton, will be: ( Given $\pi =\frac{22}{7}$ )

1. A.$360$
2. B.$180$
3. C.$1080$
4. D.$154$

A spherical soap bubble of radius 3 cm is formed inside another spherical soap bubble of radius 6 cm. If the internal pressure of the smaller bubble of radius 3 cm in the above system is equal to the internal pressure of another single soap bubble of radius r cm. The value of r is ___________.

$7\mathrm{mol}$ of a certain monoatomic ideal gas undergoes a temperature increase of $40\mathrm{K}$ at constant pressure. The increase in the internal energy of the gas in this process is : (Given $\mathrm{R}=8.3\mathrm{J}{\mathrm{K}}^{-1}\mathrm{mo}{\mathrm{l}}^{-1}$ )

1. A.$5810\mathrm{J}$
2. B.$3486\mathrm{J}$
3. C.$11620\mathrm{J}$
4. D.$6972\mathrm{J}$

A water drop of radius $1\mathrm{cm}$ is broken into $729$ equal droplets. If surface tension of water is $75dyne/cm$, then the gain in surface energy upto first decimal place will be : (Given $\pi =3.14$ )

1. A.$8.5\times 10^{-4}\mathrm{J}$
2. B.$8.2\times 10^{-4}\mathrm{J}$
3. C.$7.5\times 10^{-4}\mathrm{J}$
4. D.$5.3\times 10^{-4}\mathrm{J}$

A drop of liquid of density $\rho$ is floating half immersed in a liquid of density $\sigma$ and surface tension $7.5\times 10^{-4}{\text{ Ncm}}^{-1}$. The radius of drop in $\mathrm{cm}$ will be : ($g=10{\text{ ms}}^{-2}$)

1. A.$\frac{15}{\sqrt{(2\rho -\sigma )}}$
2. B.$\frac{15}{\sqrt{(\rho -\sigma )}}$
3. C.$\frac{3}{2\sqrt{(\rho -\sigma )}}$
4. D.$\frac{3}{20\sqrt{(2\rho -\sigma )}}$

An air bubble of negligible weight having radius r rises steadily through a solution of density $\sigma$ at speed v. The coefficient of viscosity of the solution is given by :

1. A.$\eta =\frac{4r\sigma g}{9v}$
2. B.$\eta =\frac{2r^2\sigma g}{9v}$
3. C.$\eta =\frac{2\pi r^2\sigma g}{9v}$
4. D.$\eta =\frac{2r^2\sigma g}{3\pi v}$

The pressure of the gas in a constant volume gas thermometer is $100\mathrm{cm}$ of mercury when placed in melting ice at $1\mathrm{atm}$. When the bulb is placed in a liquid, the pressure becomes $180\mathrm{cm}$ of mercury. Temperature of the liquid is : (Given $0^{\circ }\mathrm{C}=273\mathrm{K}$)

1. A.$300\mathrm{K}$
2. B.$400\mathrm{K}$
3. C.$600\mathrm{K}$
4. D.$491\mathrm{K}$

The excess pressure inside a liquid drop is $500{\text{ Nm}}^{-2}$. If the radius of the drop is $2\text{ mm}$, the surface tension of liquid is $x\times 10^{-3}{\text{ Nm}}^{-1}$. The value of $x$ is ___________.

A water drop of radius $1\mu \text{m}$ falls in a situation where the effect of buoyant force is negligible. Co-efficient of viscosity of air is $1.8\times 10^{-5}{\text{ Nsm}}^{-2}$ and its density is negligible as compared to that of water $10^6{\text{ gm}}^{-3}$. Terminal velocity of the water drop is : (Take acceleration due to gravity $=10{\text{ ms}}^{-2}$)

1. A.$145.4\times 10^{-6}{\text{ ms}}^{-1}$
2. B.$118.0\times 10^{-6}{\text{ ms}}^{-1}$
3. C.$132.6\times 10^{-6}{\text{ ms}}^{-1}$
4. D.$123.4\times 10^{-6}{\text{ ms}}^{-1}$

A liquid of density $750\mathrm{kg}{\mathrm{m}}^{-3}$ flows smoothly through a horizontal pipe that tapers in cross-sectional area from ${\mathrm{A}}_1=1.2\times 10^{-2}{\mathrm{m}}^2$ to ${\mathrm{A}}_2=\frac{A_1}{2}$. The pressure difference between the wide and narrow sections of the pipe is $4500\mathrm{Pa}$. The rate of flow of liquid is ____ $\times 10^{-3}{\mathrm{m}}^3{\mathrm{s}}^{-1}$.

A mixture of hydrogen and oxygen has volume $2000\mathrm{c}{\mathrm{m}}^3$, temperature $300\mathrm{K}$, pressure $100\mathrm{kPa}$ and mass $0.76\mathrm{g}$. The ratio of number of moles of hydrogen to number of moles of oxygen in the mixture will be: [Take gas constant $\mathrm{R}=8.3\mathrm{J}{\mathrm{K}}^{-1}\mathrm{mo}{\mathrm{l}}^{-1}$]

1. A.$\frac{1}{3}$
2. B.$\frac{3}{1}$
3. C.$\frac{1}{16}$
4. D.$\frac{16}{1}$

The current density in a cylindrical wire of radius $4\mathrm{mm}$ is $4\times 10^6\mathrm{A}{\mathrm{m}}^{-2}$. The current through the outer portion of the wire between radial distances $\frac{R}{2}$ and $R$ is ____ $\pi \mathrm{A}$.

When a ball is dropped into a lake from a height 4.9 m above the water level, it hits the water with a velocity v and then sinks to the bottom with the constant velocity v. It reaches the bottom of the lake 4.0 s after it is dropped. The approximate depth of the lake is :

1. A.19.6 m
2. B.29.4 m
3. C.39.2 m
4. D.73.5 m

1. A.$P_1>P_2$
2. B.$P_1<P_2$
3. C.$P_1=P_2$
4. D.Insufficient data to draw any conclusion

The current density in a cylindrical wire of radius $r=4.0\text{ mm}$ is $1.0\times 10^6{\text{ A/m}}^2$. The current through the outer portion of the wire between radial distances $\frac{r}{2}$ and $r$ is $x\pi \text{ A}$; where x is ________.

If $\rho$ is the density and $\eta$ is coefficient of viscosity of fluid which flows with a speed v in the pipe of diameter d, the correct formula for Reynolds number ${\mathrm{R}}_e$ is :

1. A.${\mathrm{R}}_e=\frac{\eta d}{\rho v}$
2. B.${\mathrm{R}}_e=\frac{\rho v}{\eta d}$
3. C.${\mathrm{R}}_e=\frac{\rho vd}{\eta }$
4. D.${\mathrm{R}}_e=\frac{\eta }{\rho vd}$

A heat engine operates with the cold reservoir at temperature 324 K. The minimum temperature of the hot reservoir, if the heat engine takes 300 J heat from the hot reservoir and delivers 180 J heat to the cold reservoir per cycle, is ____________ K.

The velocity of upper layer of water in a river is $36{\text{ kmh}}^{-1}$. Shearing stress between horizontal layers of water is $10^{-3}{\text{ Nm}}^{-2}$. Depth of the river is $\underline{}\text{ m}$. (Co-efficient of viscosity of water is $10^{-2}\text{ Pa.s}$)

When a gas filled in a closed vessel is heated by raising the temperature by $1^{\circ }\mathrm{C}$, its pressure increases by $0.4\%$. The initial temperature of the gas is ____ $\mathrm{K}$.

A cylindrical container of volume $4.0\times 10^{-3}{\text{ m}}^3$ contains one mole of hydrogen and two moles of carbon dioxide. Assume the temperature of the mixture is $400\text{ K}$. The pressure of the mixture of gases is : [Take gas constant as $8.3{\text{ J mol}}^{-1}{\text{ K}}^{-1}$]

1. A.$249\times 10^1\text{ Pa}$
2. B.$24.9\times 10^3\text{ Pa}$
3. C.$24.9\times 10^5\text{ Pa}$
4. D.$24.9\text{ Pa}$

A raindrop with radius R = 0.2 mm falls from a cloud at a height h = 2000 m above the ground. Assume that the drop is spherical throughout its fall and the force of buoyance may be neglected, then the terminal speed attained by the raindrop is : [Density of water $f_w=1000\mathrm{kg}{\mathrm{m}}^{-3}$ and Density of air $f_a=1.2\mathrm{kg}{\mathrm{m}}^{-3}$, g = $10m/{\mathrm{s}}^2$, Coefficient of viscosity of air = $1.8\times 10^{-5}\mathrm{Ns}{\mathrm{m}}^{-2}$]

1. A.$250.6\mathrm{m}{\mathrm{s}}^{-1}$
2. B.$43.56\mathrm{m}{\mathrm{s}}^{-1}$
3. C.$4.94\mathrm{m}{\mathrm{s}}^{-1}$
4. D.$14.4\mathrm{m}{\mathrm{s}}^{-1}$