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. $2\frac{1}{3}W$

The relative density of ice is 0.9 and that of sea water is 1.125. What fraction of the whole volume of an iceberg appears above the surface of the sea?

1. 1/5

2. 2/5

3. 3/5

4. 4/5

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. $\sqrt{\frac{3}{2}}$