Water is flowing continuously from a tap having an internal diameter 8 x 10^-3 m. The water velocity as it leaves the tap is 0.4 ms^-1. The diameter of the water stream at a distance 2 x 10^-1 m below the tap is close to

1. 5.0 x 10^-3 m

2. 7.5 x 10^-3 m

3. 9.6 x 10^-3 m

4. 3.6 x 10^-3 m

Two metal spheres are falling through a liquid of density $2\times {10}^3\mathrm{kg}/{\mathrm{m}}^3$ with the same uniform speed. The material density of sphere 1 and sphere 2 are $8\times {10}^3\mathrm{kg}/{\mathrm{m}}^3$ and $11\times {10}^3\mathrm{kg}/{\mathrm{m}}^3$ respectively. The ratio of their radii is

1. $\frac{11}{8}$

2. $\sqrt{\frac{11}{8}}$

3. $\frac{3}{2}$

4. $\sqrt{\frac{3}{2}}$

A long cylindrical glass vessel has a small hole of radius r at its bottom. The depth to which the vessel can be lowered vertically in a deep water bath without any water entering inside is (surface tension = T and d = density of water)

1. $\frac{4\mathrm{T}}{\text{ rdg }}$

2. $\frac{5\mathrm{T}}{\text{ rdg }}$

3. $\frac{3\mathrm{T}}{\text{ rdg }}$

4. $\frac{2\mathrm{T}}{\text{ rdg }}$

A candle of diameter d is floating on a liquid in a cylindrical container of diameter D (D>>d) as shown in figure. If it is buming at the rate of 2 cm/hour then the top of the candle will

1. remain at the same height

2. fall at the rate of 1 cm/hour

3. fall at the rate of 2cm/hour

4. go up the rate of 1 cm/hour

A ball of relative density 0.8 falls into water from a height of 2 m. The depth to which the ball will sink is (neglect viscous forces)

1. 8 m

2. 2 m

3. 6 m

4. 16 m

In the given figure, the velocity v₃ will be

1. 2 m/s

2. 4 m/s

3. 1 m/s

4. 3 m/s

There is hole of area a at the bottom of a cylindrical of area A. Water is filled upto a height h and water flows out in t second. If water is filled to a height 4h, it will flow out in time

1. $\frac{t}{4}$

2. 2t

3. 4t

4. $\frac{t}{2}$

There is a hole in the bottom of tank having water. If total pressure at bottom is 3 atm $(1 \mathrm{atm}={10}^5\mathrm{N}/{\mathrm{m}}^2)$ then the velocity of water flowing from hole is

1. $\sqrt{400} m/s$

2. $\sqrt{600} m/s$

3. $\sqrt{60} m/s$

4. None of these

The reading of spring balance when a block is suspended from it in air, is 6 N. This reading is changed to 40 N when the block is immersed in water. The specific gravity of the block is

1. 3

2. 2

3. 6

4. $\frac{3}{2}$

If work W is done in blowing a bubble of radius R from soap solution, then the work done in blowing a bubble of radius 2R from the same solution is

1. W/2

2. 2W

3. 4W

4. $2\frac{1}{3}W$