1
IIT-JEE 2008 Paper 1 Offline
+3
-1

STATEMENT - 1 :

The stream of water flowing at high speed from a garden hose pipe tends to spread line a fountain when held vertically up, but tends to narrow down when held vertically down.

and

STATEMENT - 2 :

In any steady flow of an incompressible fluid, the volume flow rate of the fluid remains constant.

A
Statement - 1 is True, Statement - 2 is True; Statement - 2 is a correct explanation for Statement - 1
B
Statement - 1 is True, Statement - 2 is True; Statement - 2 is NOT a correct explanation for Statement - 1
C
Statement - 1 is True, Statement - 2 is False
D
Statement - 1 is False, Statement - 2 is True
2
IIT-JEE 2008 Paper 1 Offline
+3
-1

A small spherical monoatomic ideal gas bubble $$\left( {\gamma = {5 \over 3}} \right)$$ is trapped inside a liquid of density $$\rho_1$$ (see figure). Assume that the bubble does not exchange any heat with the liquid. The bubble contains n moles of gas. The temperature of the gas when the bubble is at the bottom is T$$_0$$, the height of the liquid is H and the atmospheric pressure is P$$_0$$ (Neglect surface tension)

As the bubble moves upwards, besides the buoyancy force the following forces are acting on it

A
Only the force of gravity
B
The force due to gravity and the force due to the pressure of the liquid
C
The force due to gravity, the force due to the pressure of the liquid and the force due to viscosity of the liquid
D
The force due to gravity and the force due to viscosity of the liquid
3
IIT-JEE 2008 Paper 1 Offline
+3
-1

A small spherical monoatomic ideal gas bubble $$\left( {\gamma = {5 \over 3}} \right)$$ is trapped inside a liquid of density $$\rho_1$$ (see figure). Assume that the bubble does not exchange any heat with the liquid. The bubble contains n moles of gas. The temperature of the gas when the bubble is at the bottom is T$$_0$$, the height of the liquid is H and the atmospheric pressure is P$$_0$$ (Neglect surface tension)

When the gas bubble is at a height y from the bottom, its temperature is :

A
$${T_0}{\left( {{{{P_0} + {\rho _l}gH} \over {{P_0} + {\rho _l}gy}}} \right)^{{2 \over 5}}}$$
B
$${T_0}{\left( {{{{P_0} + {\rho _l}g(H - y)} \over {{P_0} + {\rho _l}gH}}} \right)^{{2 \over 5}}}$$
C
$${T_0}{\left( {{{{P_0} + {\rho _l}gH} \over {{P_0} + {\rho _l}gy}}} \right)^{{3 \over 5}}}$$
D
$${T_0}{\left( {{{{P_0} + {\rho _l}g(H - y)} \over {{P_0} + {\rho _l}gH}}} \right)^{{3 \over 5}}}$$
4
IIT-JEE 2008 Paper 1 Offline
+3
-1

A small spherical monoatomic ideal gas bubble $$\left( {\gamma = {5 \over 3}} \right)$$ is trapped inside a liquid of density $$\rho_1$$ (see figure). Assume that the bubble does not exchange any heat with the liquid. The bubble contains n moles of gas. The temperature of the gas when the bubble is at the bottom is T$$_0$$, the height of the liquid is H and the atmospheric pressure is P$$_0$$ (Neglect surface tension)

The buoyancy force acting on the gas bubble is (Assume R is the universal gas constant)

A
$${\rho _l}nRg{T_0}{{{{({P_0} + {\rho _l}gH)}^{{2 \over 5}}}} \over {{{({P_0} + {\rho _l}gy)}^{{7 \over 5}}}}}$$
B
$${{{\rho _l}nRg{T_0}} \over {{{({P_0} + {\rho _l}gH)}^{{2 \over 5}}}{{[{P_0} + {\rho _l}g(H - y)]}^{{3 \over 5}}}}}$$
C
$${\rho _l}nRg{T_0}{{{{({P_0} + {\rho _l}gH)}^{{3 \over 5}}}} \over {{{({P_0} + {\rho _l}gy)}^{{8 \over 5}}}}}$$
D
$${{{\rho _l}nRg{T_0}} \over {{{({P_0} + {\rho _l}gH)}^{{3 \over 5}}}[{P_0} + {\rho _l}g{{(H - y)}^{{2 \over 5}}}}}$$
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