1
JEE Advanced 2014 Paper 2 Offline
+3
-1

A glass capillary tube is of the shape of truncated cone with an apex angle $$\alpha$$ so that its two ends have cross sections of different radii. When dipped in water vertically, water rises in it to a height h, where the radius of its cross section is b. If the surface tension of water is S, its density is $$\rho$$, and its contact angle with glass is $$\theta$$, the value of h will be (g is the acceleration due to gravity)

A
$${{2S} \over {b\rho g}}\cos (\theta - \alpha )$$
B
$${{2S} \over {b\rho g}}\cos (\theta + \alpha )$$
C
$${{2S} \over {b\rho g}}\cos (\theta - \alpha /2)$$
D
$${{2S} \over {b\rho g}}\cos (\theta + \alpha /2)$$
2
JEE Advanced 2014 Paper 2 Offline
+3
-1

A spray gun is shown in the below figure where a piston pushes air out of a nozzle. A thin tube of uniform cross-section is connected to the nozzle. The other end of the tube is in a small liquid container. As the piston pushes air through the nozzle, the liquid from the container rises into the nozzle and is sprayed out. For the spray gun shown, the radii of the piston and the nozzle are 20 mm and 1 mm, respectively. The upper end of the container is open to the atmosphere.

If the piston is pushed at a speed of 5 mm s$$-$$1, the air comes out of the nozzle with a speed of

A
$0.1 \mathrm{~ms}^{-1}$
B
$1 \mathrm{~ms}^{-1}$
C
$2 \mathrm{~ms}^{-1}$
D
$8 \mathrm{~ms}^{-1}$
3
JEE Advanced 2014 Paper 2 Offline
+3
-1

A spray gun is shown in the below figure where a piston pushes air out of a nozzle. A thin tube of uniform cross-section is connected to the nozzle. The other end of the tube is in a small liquid container. As the piston pushes air through the nozzle, the liquid from the container rises into the nozzle and is sprayed out. For the spray gun shown, the radii of the piston and the nozzle are 20 mm and 1 mm, respectively. The upper end of the container is open to the atmosphere.

If the density of air is $$\rho$$a and that of the liquid $$\rho$$l, then for a given piston speed the rate (volume per unit time) at which the liquid is sprayed will be proportional to

A
$\sqrt{\frac{\rho_a}{\rho_{\ell}}}$
B
$\sqrt{\rho_a \rho_{\ell}}$
C
$\sqrt{\frac{\rho_{\ell}}{\rho_a}}$
D
$\rho_{\ell}$
4
JEE Advanced 2013 Paper 1 Offline
+2
-0.5
One end of a horizontal thick copper wire of length 2L and radius 2R is welded to an end of another horizontal thin copper wire of length L and radius R. When the arrangement is stretched by applying forces at two ends, the ratio of the elongation in the thin wire to that in the thick wire is
A
0.25
B
0.50
C
2.00
D
4.00
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