1
AIEEE 2008
+4
-1
A spherical solid ball of volume $$V$$ is made of a material of density $${\rho _1}$$. It is falling through a liquid of density $${\rho _2}\left( {{\rho _2} < {\rho _1}} \right)$$. Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed $$v,$$ i.e., $${F_{viscous}} = - k{v^2}\left( {k > 0} \right).$$ The terminal speed of the ball is
A
$$\sqrt {{{Vg\left( {{\rho _1} - {\rho _2}} \right)} \over k}}$$
B
$${{{Vg{\rho _1}} \over k}}$$
C
$$\sqrt {{{Vg{\rho _1}} \over k}}$$
D
$${{Vg\left( {{\rho _1} - {\rho _2}} \right)} \over k}$$
2
AIEEE 2008
+4
-1
A capillary tube (A) is dipped in water. Another identical tube (B) is dipped in a soap-water solution. Which of the following shows the relative nature of the liquid columns in the two tubes?
A
B
C
D
3
AIEEE 2008
+4
-1
A jar is filled with two non-mixing liquids $$1$$ and $$2$$ having densities $${\rho _1}$$ and $${\rho _2}$$ respectively. A solid ball, made of a material of density $${\rho _3}$$, is dropped in the jar. It comes to equilibrium in the position shown in the figure. Which of the following is true for $${\rho _1}$$ , $${\rho _1}$$ and $${\rho _3}$$ ?
A
$${\rho _3} < {\rho _1} < \rho {}_2$$
B
$${\rho _1} > {\rho _3} > \rho {}_2$$
C
$${\rho _1} < {\rho _2} < \rho {}_3$$
D
$${\rho _1} < {\rho _3} < \rho {}_2$$
4
AIEEE 2006
+4
-1
If the terminal speed of a sphere of gold (density $$= 19.5\,\,kg/{m^3}$$) is $$0.2$$ $$m/s$$ in a viscous liquid (density $$= 1.5\,\,kg/{m^3}$$, find the terminal speed of a sphere of silver (density $$= 10.5\,\,kg/{m^3}$$) of the same size in the same liquid
A
$$0.4$$ $$m/s$$
B
$$0.133$$ $$m/s$$
C
$$0.1$$ $$m/s$$
D
$$0.2$$ $$m/s$$
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