A tank is filled to a height H. The range of water coming out of a hole which is a depth H/4 from the surface of water level is

1. $\frac{2H}{\sqrt{3}}$

2. $\frac{\sqrt{3}H}{2}$

3. $\sqrt{3}H$

4. $\frac{3H}{4}$

Two rain drops falling through air have radii in the ratio 1:2. They will have terminal velocity in the ratio

1. 4:1

2. 1:4

3. 2:1

4. 1:2

Block A in the figure shown here hangs by a cord from dynamometer (spring balance) $D_1$ and is submerged in a liquid C contained in beaker B. The mass of beakerr is 1 kg and the mass of liquid is 1.5kg. The readings of dynamometers $D_1$ and $D_2$ of block A is pulled up out of the liquid?

1. $D_1$ will read 5 kg & $D_2$ will also read 5 kg

2. $D_1$ will read 7.5 kg & $D_2$ will read 2.5 kg

3. $D_1$ will read 2.5 kg & $D_2$ will also read 7.5 kg

4. $D_1$ will read 10 kg & $D_2$ will also read 2.5 kg

A ring is cut from a platinum tube having 8.5cm internal and 8.7 cm extrenal diameter. It is supported horizontally from a pan of a balance so that it comes in contact with the water in glass vessel. If an extra 3.97 gram weight is required to pull it away from water, the durface tension of water is

1. 72.07 dyne per cm

2. 70.80 dyne per cm

3. 65.35 dyne per cm

4.  60.00 dyne per cm

A number of water droplets each of radius r coalesce to form a drop of radius R. Are consuming the whole of the energy liberated due to  coalescence goes into hitting the drop, the rise and temperature $\mathrm{d\theta }$, is

1. $\frac{2\mathrm{T}}{\mathrm{r} \mathrm{J}}$

2. $\frac{3\mathrm{T}}{\mathrm{r} \mathrm{J}}$

3. $\frac{3\mathrm{T}}{\mathrm{J}}\left(\frac{1}{\mathrm{r}}-\frac{1}{\mathrm{R}}\right)$

4. $\frac{3\mathrm{T}}{\mathrm{J}}\left(\frac{1}{\mathrm{r}}+\frac{1}{\mathrm{R}}\right)$

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

1. More than filled if ${\rho }_c$ is less than 0.5

2. More than half filled if ${\rho }_c$ is less than 1.0

3. Half filled if ${\rho }_c$ is less than 0.5

4. Less than half filled if ${\rho }_c$ is less than 0.5

A large tank is filled with water (density= ${10}^3 \mathrm{kg}/{\mathrm{m}}^3$). A small hole is made at a depth 10m below water surface. The range of water issuing out of  the hole is R on ground. What extra p[ressure must be applied on the water surface so that the range become 2R (take 1 atm = ${10}^5$ Pa and g= 10 m/${\mathrm{s}}^2$)

1. a atm

2. 2 atm

3. 4 atm

4. 3 atm

When a block of iron floats in mercury at 0$°$C, a fraction $k_1$ of its volume is submerged, while at 60$°$C, a fraction $k_2$ is seen to be submerged, If the coefficient of volume expansion of iron is ${\mathrm{\gamma }}_{\mathrm{Fe}}$ and that of mercury is ${\gamma }_{Hg}$, then the ratio of $k_1$/$k_2$ can be expressed as

1. $\frac{1+{{60}_{\gamma }}_{Fe}}{1+{{60}_{\gamma }}_{He}}$

2. $\frac{1-{{60}_{\gamma }}_{Fe}}{1+{{60}_{\gamma }}_{He}}$

3. $\frac{1+{{60}_{\gamma }}_{Fe}}{1-{{60}_{\gamma }}_{He}}$

4. $\frac{1+{{60}_{\gamma }}_{Hg}}{1+{{60}_{\gamma }}_{Fe}}$

The diameter of a big drop of water is 2.8 mm. It is broken into 125 equal drops. If the surface tension of water is 75 dyne/cm, then the work done is

1. zero

2. 19 erg

3. 46 erg

4. 74 erg

If pressure at half the depth of a lake is equal to 2/3 pressure at the botom of the lake then what is the depth of the lake

1. 10 m

2. 20 m

3. 60 m

4. 30 m