143028
If two soap bubbles of different radii are in communication with each other.
1 air flows from larger bubble into the smaller one
2 the size of the bubbles remains the same
3 air flows from the smaller bubble into the larger one and the larger bubble grows at the expense of the smaller one
4 the air flows from the larger
Explanation:
C Excess of pressure in a soap bubble $\mathrm{p}=$ $\frac{4 T}{R}$ where, $T$ is surface tension of soap solution and $R$ is the radius of the bubble. $\mathrm{p} \propto \frac{1}{\mathrm{R}}$ Therefore, pressure is greater in soap bubble of smaller radius. Hence, air will flow from the smaller bubble into the larger bubble and the larger bubble grows at the expense of the smaller one.
CG PET- 2007
Mechanical Properties of Fluids
143057
The excess pressure inside a soap bubble that of $5 \mathrm{~cm}$ in diameter, assuming $0.026 \mathrm{~N} \mathrm{~m}^{-1}$ as the surface tension of the soap solution is
143069
A rain drop of radius $R$ falls from a height of $H$ metre above the ground. The work done by the gravitational force is proportion to which one of the following?
1 $\mathrm{R}^{2}$
2 $\mathrm{R}^{3}$
3 $\mathrm{R}$
4 $\mathrm{R}^{1 / 2}$
Explanation:
B Given, Rain drop of radius $=\mathrm{R}$, height $=\mathrm{H}$ Work done $=$ Change in P.E. $\mathrm{W} =\mathrm{mgH}$ $=\rho \times \mathrm{VgH}$ $=\rho \times \frac{4}{3} \pi \mathrm{R}^{3} \times \mathrm{gH}$ Hence, $\mathrm{W} \propto \mathrm{R}^{3}$
WB JEE-2007
Mechanical Properties of Fluids
143070
The ratio of radii of two bubbled is $2: 1$, What is the ratio of excess pressures inside them?
1 $1: 2$
2 $1: 4$
3 $2: 1$
4 $4: 1$
Explanation:
A Given, $\frac{\mathrm{r}_{1}}{\mathrm{r}_{2}}=\frac{2}{1}$ The excess pressure inside the bubble, $\Rightarrow \quad \mathrm{P}=\frac{4 \mathrm{~T}}{\mathrm{r}} \Rightarrow \mathrm{P} \propto \frac{1}{\mathrm{r}}$ $\Rightarrow \quad \frac{\mathrm{P}_{1}}{\mathrm{P}_{2}} =\frac{\mathrm{r}_{2}}{\mathrm{r}_{1}}$ $\Rightarrow \quad \frac{\mathrm{P}_{1}}{\mathrm{P}_{2}} =\frac{1}{2}$
UP CPMT-2012
Mechanical Properties of Fluids
143093
The terminal velocity $\left(v_{t}\right)$ of the spherical rain drop depends on the radius $(r)$ of the spherical rain drop as :
1 $r^{1 / 2}$
2 $\mathrm{r}$
3 $r^{2}$
4 $r^{3}$
Explanation:
C We know that, Terminal velocity $\left(v_{t}\right)$ is - $v_{\mathrm{t}}=\frac{2}{9} \frac{\mathrm{r}^{2}(\sigma-\rho) \mathrm{g}}{\eta}$ $v_{\mathrm{t}} \propto \mathrm{r}^{2}$ Hence, it is clear that $v_{\mathrm{t}}$ of spherical rain drop depends on the $r^{2}$ of spherical rain drop.
143028
If two soap bubbles of different radii are in communication with each other.
1 air flows from larger bubble into the smaller one
2 the size of the bubbles remains the same
3 air flows from the smaller bubble into the larger one and the larger bubble grows at the expense of the smaller one
4 the air flows from the larger
Explanation:
C Excess of pressure in a soap bubble $\mathrm{p}=$ $\frac{4 T}{R}$ where, $T$ is surface tension of soap solution and $R$ is the radius of the bubble. $\mathrm{p} \propto \frac{1}{\mathrm{R}}$ Therefore, pressure is greater in soap bubble of smaller radius. Hence, air will flow from the smaller bubble into the larger bubble and the larger bubble grows at the expense of the smaller one.
CG PET- 2007
Mechanical Properties of Fluids
143057
The excess pressure inside a soap bubble that of $5 \mathrm{~cm}$ in diameter, assuming $0.026 \mathrm{~N} \mathrm{~m}^{-1}$ as the surface tension of the soap solution is
143069
A rain drop of radius $R$ falls from a height of $H$ metre above the ground. The work done by the gravitational force is proportion to which one of the following?
1 $\mathrm{R}^{2}$
2 $\mathrm{R}^{3}$
3 $\mathrm{R}$
4 $\mathrm{R}^{1 / 2}$
Explanation:
B Given, Rain drop of radius $=\mathrm{R}$, height $=\mathrm{H}$ Work done $=$ Change in P.E. $\mathrm{W} =\mathrm{mgH}$ $=\rho \times \mathrm{VgH}$ $=\rho \times \frac{4}{3} \pi \mathrm{R}^{3} \times \mathrm{gH}$ Hence, $\mathrm{W} \propto \mathrm{R}^{3}$
WB JEE-2007
Mechanical Properties of Fluids
143070
The ratio of radii of two bubbled is $2: 1$, What is the ratio of excess pressures inside them?
1 $1: 2$
2 $1: 4$
3 $2: 1$
4 $4: 1$
Explanation:
A Given, $\frac{\mathrm{r}_{1}}{\mathrm{r}_{2}}=\frac{2}{1}$ The excess pressure inside the bubble, $\Rightarrow \quad \mathrm{P}=\frac{4 \mathrm{~T}}{\mathrm{r}} \Rightarrow \mathrm{P} \propto \frac{1}{\mathrm{r}}$ $\Rightarrow \quad \frac{\mathrm{P}_{1}}{\mathrm{P}_{2}} =\frac{\mathrm{r}_{2}}{\mathrm{r}_{1}}$ $\Rightarrow \quad \frac{\mathrm{P}_{1}}{\mathrm{P}_{2}} =\frac{1}{2}$
UP CPMT-2012
Mechanical Properties of Fluids
143093
The terminal velocity $\left(v_{t}\right)$ of the spherical rain drop depends on the radius $(r)$ of the spherical rain drop as :
1 $r^{1 / 2}$
2 $\mathrm{r}$
3 $r^{2}$
4 $r^{3}$
Explanation:
C We know that, Terminal velocity $\left(v_{t}\right)$ is - $v_{\mathrm{t}}=\frac{2}{9} \frac{\mathrm{r}^{2}(\sigma-\rho) \mathrm{g}}{\eta}$ $v_{\mathrm{t}} \propto \mathrm{r}^{2}$ Hence, it is clear that $v_{\mathrm{t}}$ of spherical rain drop depends on the $r^{2}$ of spherical rain drop.
143028
If two soap bubbles of different radii are in communication with each other.
1 air flows from larger bubble into the smaller one
2 the size of the bubbles remains the same
3 air flows from the smaller bubble into the larger one and the larger bubble grows at the expense of the smaller one
4 the air flows from the larger
Explanation:
C Excess of pressure in a soap bubble $\mathrm{p}=$ $\frac{4 T}{R}$ where, $T$ is surface tension of soap solution and $R$ is the radius of the bubble. $\mathrm{p} \propto \frac{1}{\mathrm{R}}$ Therefore, pressure is greater in soap bubble of smaller radius. Hence, air will flow from the smaller bubble into the larger bubble and the larger bubble grows at the expense of the smaller one.
CG PET- 2007
Mechanical Properties of Fluids
143057
The excess pressure inside a soap bubble that of $5 \mathrm{~cm}$ in diameter, assuming $0.026 \mathrm{~N} \mathrm{~m}^{-1}$ as the surface tension of the soap solution is
143069
A rain drop of radius $R$ falls from a height of $H$ metre above the ground. The work done by the gravitational force is proportion to which one of the following?
1 $\mathrm{R}^{2}$
2 $\mathrm{R}^{3}$
3 $\mathrm{R}$
4 $\mathrm{R}^{1 / 2}$
Explanation:
B Given, Rain drop of radius $=\mathrm{R}$, height $=\mathrm{H}$ Work done $=$ Change in P.E. $\mathrm{W} =\mathrm{mgH}$ $=\rho \times \mathrm{VgH}$ $=\rho \times \frac{4}{3} \pi \mathrm{R}^{3} \times \mathrm{gH}$ Hence, $\mathrm{W} \propto \mathrm{R}^{3}$
WB JEE-2007
Mechanical Properties of Fluids
143070
The ratio of radii of two bubbled is $2: 1$, What is the ratio of excess pressures inside them?
1 $1: 2$
2 $1: 4$
3 $2: 1$
4 $4: 1$
Explanation:
A Given, $\frac{\mathrm{r}_{1}}{\mathrm{r}_{2}}=\frac{2}{1}$ The excess pressure inside the bubble, $\Rightarrow \quad \mathrm{P}=\frac{4 \mathrm{~T}}{\mathrm{r}} \Rightarrow \mathrm{P} \propto \frac{1}{\mathrm{r}}$ $\Rightarrow \quad \frac{\mathrm{P}_{1}}{\mathrm{P}_{2}} =\frac{\mathrm{r}_{2}}{\mathrm{r}_{1}}$ $\Rightarrow \quad \frac{\mathrm{P}_{1}}{\mathrm{P}_{2}} =\frac{1}{2}$
UP CPMT-2012
Mechanical Properties of Fluids
143093
The terminal velocity $\left(v_{t}\right)$ of the spherical rain drop depends on the radius $(r)$ of the spherical rain drop as :
1 $r^{1 / 2}$
2 $\mathrm{r}$
3 $r^{2}$
4 $r^{3}$
Explanation:
C We know that, Terminal velocity $\left(v_{t}\right)$ is - $v_{\mathrm{t}}=\frac{2}{9} \frac{\mathrm{r}^{2}(\sigma-\rho) \mathrm{g}}{\eta}$ $v_{\mathrm{t}} \propto \mathrm{r}^{2}$ Hence, it is clear that $v_{\mathrm{t}}$ of spherical rain drop depends on the $r^{2}$ of spherical rain drop.
143028
If two soap bubbles of different radii are in communication with each other.
1 air flows from larger bubble into the smaller one
2 the size of the bubbles remains the same
3 air flows from the smaller bubble into the larger one and the larger bubble grows at the expense of the smaller one
4 the air flows from the larger
Explanation:
C Excess of pressure in a soap bubble $\mathrm{p}=$ $\frac{4 T}{R}$ where, $T$ is surface tension of soap solution and $R$ is the radius of the bubble. $\mathrm{p} \propto \frac{1}{\mathrm{R}}$ Therefore, pressure is greater in soap bubble of smaller radius. Hence, air will flow from the smaller bubble into the larger bubble and the larger bubble grows at the expense of the smaller one.
CG PET- 2007
Mechanical Properties of Fluids
143057
The excess pressure inside a soap bubble that of $5 \mathrm{~cm}$ in diameter, assuming $0.026 \mathrm{~N} \mathrm{~m}^{-1}$ as the surface tension of the soap solution is
143069
A rain drop of radius $R$ falls from a height of $H$ metre above the ground. The work done by the gravitational force is proportion to which one of the following?
1 $\mathrm{R}^{2}$
2 $\mathrm{R}^{3}$
3 $\mathrm{R}$
4 $\mathrm{R}^{1 / 2}$
Explanation:
B Given, Rain drop of radius $=\mathrm{R}$, height $=\mathrm{H}$ Work done $=$ Change in P.E. $\mathrm{W} =\mathrm{mgH}$ $=\rho \times \mathrm{VgH}$ $=\rho \times \frac{4}{3} \pi \mathrm{R}^{3} \times \mathrm{gH}$ Hence, $\mathrm{W} \propto \mathrm{R}^{3}$
WB JEE-2007
Mechanical Properties of Fluids
143070
The ratio of radii of two bubbled is $2: 1$, What is the ratio of excess pressures inside them?
1 $1: 2$
2 $1: 4$
3 $2: 1$
4 $4: 1$
Explanation:
A Given, $\frac{\mathrm{r}_{1}}{\mathrm{r}_{2}}=\frac{2}{1}$ The excess pressure inside the bubble, $\Rightarrow \quad \mathrm{P}=\frac{4 \mathrm{~T}}{\mathrm{r}} \Rightarrow \mathrm{P} \propto \frac{1}{\mathrm{r}}$ $\Rightarrow \quad \frac{\mathrm{P}_{1}}{\mathrm{P}_{2}} =\frac{\mathrm{r}_{2}}{\mathrm{r}_{1}}$ $\Rightarrow \quad \frac{\mathrm{P}_{1}}{\mathrm{P}_{2}} =\frac{1}{2}$
UP CPMT-2012
Mechanical Properties of Fluids
143093
The terminal velocity $\left(v_{t}\right)$ of the spherical rain drop depends on the radius $(r)$ of the spherical rain drop as :
1 $r^{1 / 2}$
2 $\mathrm{r}$
3 $r^{2}$
4 $r^{3}$
Explanation:
C We know that, Terminal velocity $\left(v_{t}\right)$ is - $v_{\mathrm{t}}=\frac{2}{9} \frac{\mathrm{r}^{2}(\sigma-\rho) \mathrm{g}}{\eta}$ $v_{\mathrm{t}} \propto \mathrm{r}^{2}$ Hence, it is clear that $v_{\mathrm{t}}$ of spherical rain drop depends on the $r^{2}$ of spherical rain drop.
143028
If two soap bubbles of different radii are in communication with each other.
1 air flows from larger bubble into the smaller one
2 the size of the bubbles remains the same
3 air flows from the smaller bubble into the larger one and the larger bubble grows at the expense of the smaller one
4 the air flows from the larger
Explanation:
C Excess of pressure in a soap bubble $\mathrm{p}=$ $\frac{4 T}{R}$ where, $T$ is surface tension of soap solution and $R$ is the radius of the bubble. $\mathrm{p} \propto \frac{1}{\mathrm{R}}$ Therefore, pressure is greater in soap bubble of smaller radius. Hence, air will flow from the smaller bubble into the larger bubble and the larger bubble grows at the expense of the smaller one.
CG PET- 2007
Mechanical Properties of Fluids
143057
The excess pressure inside a soap bubble that of $5 \mathrm{~cm}$ in diameter, assuming $0.026 \mathrm{~N} \mathrm{~m}^{-1}$ as the surface tension of the soap solution is
143069
A rain drop of radius $R$ falls from a height of $H$ metre above the ground. The work done by the gravitational force is proportion to which one of the following?
1 $\mathrm{R}^{2}$
2 $\mathrm{R}^{3}$
3 $\mathrm{R}$
4 $\mathrm{R}^{1 / 2}$
Explanation:
B Given, Rain drop of radius $=\mathrm{R}$, height $=\mathrm{H}$ Work done $=$ Change in P.E. $\mathrm{W} =\mathrm{mgH}$ $=\rho \times \mathrm{VgH}$ $=\rho \times \frac{4}{3} \pi \mathrm{R}^{3} \times \mathrm{gH}$ Hence, $\mathrm{W} \propto \mathrm{R}^{3}$
WB JEE-2007
Mechanical Properties of Fluids
143070
The ratio of radii of two bubbled is $2: 1$, What is the ratio of excess pressures inside them?
1 $1: 2$
2 $1: 4$
3 $2: 1$
4 $4: 1$
Explanation:
A Given, $\frac{\mathrm{r}_{1}}{\mathrm{r}_{2}}=\frac{2}{1}$ The excess pressure inside the bubble, $\Rightarrow \quad \mathrm{P}=\frac{4 \mathrm{~T}}{\mathrm{r}} \Rightarrow \mathrm{P} \propto \frac{1}{\mathrm{r}}$ $\Rightarrow \quad \frac{\mathrm{P}_{1}}{\mathrm{P}_{2}} =\frac{\mathrm{r}_{2}}{\mathrm{r}_{1}}$ $\Rightarrow \quad \frac{\mathrm{P}_{1}}{\mathrm{P}_{2}} =\frac{1}{2}$
UP CPMT-2012
Mechanical Properties of Fluids
143093
The terminal velocity $\left(v_{t}\right)$ of the spherical rain drop depends on the radius $(r)$ of the spherical rain drop as :
1 $r^{1 / 2}$
2 $\mathrm{r}$
3 $r^{2}$
4 $r^{3}$
Explanation:
C We know that, Terminal velocity $\left(v_{t}\right)$ is - $v_{\mathrm{t}}=\frac{2}{9} \frac{\mathrm{r}^{2}(\sigma-\rho) \mathrm{g}}{\eta}$ $v_{\mathrm{t}} \propto \mathrm{r}^{2}$ Hence, it is clear that $v_{\mathrm{t}}$ of spherical rain drop depends on the $r^{2}$ of spherical rain drop.
