1
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
$\rho_{\ell}$
2
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
3
IIT-JEE 2012 Paper 2 Offline
+3
-0.75
A thin uniform cylindrical shell, closed at both ends, is partially filled with water. It is floating vertically in water in half-submerged state. If $${\rho _c}$$ is the relative density of the material of the shell with respect to water, then the correct statement is that the shell is
A
more than half-filled if $${\rho _c}$$ is less than 0.5.
B
more than half-filled if $${\rho _c}$$ is more than 1.0.
C
half-filled if $${\rho _c}$$ is more than 0.5.
D
less than half-filled if $${\rho _c}$$ is less than 0.5.
4
IIT-JEE 2010 Paper 2 Offline
+3
-0.75
When liquid medicine of density $$\rho$$ is to be put in the eye, it is done with the help of a dropper. As the bulb on the top of the dropper is pressed, a drop forms at the opening of the dropper. We wish to estimate the size of the drop. We first assume that the drop formed at the opening is spherical because that requires a minimum increase in its surface energy. To determine the size, we calculate the net vertical force due to the surface tension T when the radius of the drop is R. When the force becomes smaller than the weight of the drop, the drop gets detached from the dropper.

If the radius of the opening of the dropper is $$r$$, the vertical force due to the surface tension on the drop of radius R (assuming $$r$$ << R) is

A
$$2\pi rT$$
B
$$2\pi RT$$
C
$${{2\pi {r^2}T} \over R}$$
D
$${{2\pi {R^2}T} \over r}$$
EXAM MAP
Medical
NEET