Three liquids of densioties d, 2d and 3d are mixed in equal proportions of weights. The relatice density of the mixture is

1. $\frac{11}{7}\mathrm{d}$

2. $\frac{18}{11}\mathrm{d}$

3. $\frac{13}{9}\mathrm{d}$

4.  $\frac{23}{18}\mathrm{d}$

 A capillary tube is dipped in a liquid. Let pressure at point A, B and C be $p_{A\text{'}} p_{B\text{'}} p_C$ respectively then

1. $p_A=p_B=p_C$

2. $p_A=p_B<p_C$

3. $p_A=p_C<p_B$

4. $p_A=p_C>p_B$

 For the arrangement shown in the figure, the force at the bottom of the vessel is

1. 200 N

2. 100 N

3. 20 N

4. 2 N

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