1
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
$${{2\pi {R^2}T} \over r}$$
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 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
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.

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
4
IIT-JEE 2010 Paper 2 Offline
Numerical
+3
-0
A diatomic ideal gas is compressed adiabatically $${1 \over {32}}$$ of its initial volume. If the initial temperature of the gas is Ti (in Kelvin) and the final temperature is a Ti, the value of $$a$$ is