1
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.
2
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
$${{2\pi {R^2}T} \over r}$$
3
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 r = 5 $$\times$$ 10−4 m, $$\rho$$ = 103 kg m−3 , g = 10 m/s2 , T = 0.11 Nm−1 , the radius of the drop when it detaches from the dropper is approximately

A
1.4 $$\times$$ 10−3 m
B
3.3 $$\times$$ 10−3 m
C
2.0 $$\times$$ 10−3 m
D
4.1 $$\times$$ 10−3 m
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.

After the drop detaches, its surface energy is

A
1.4 $$\times$$ 10−6 J
B
2.7 $$\times$$ 10−6 J
C
5.4 $$\times$$ 10−6 J
D
8.1 $$\times$$ 10−6 J
EXAM MAP
Medical
NEET