A large number of liquid drops each of radius r coalesce to form a single drop of radius R. The energy released in the process is converted into the kinetic energy of the big drop so formed. The speed of the big drop is(given surface tension of liquid is T, density of liquid is $\rho$)

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

2. $\sqrt{\frac{2\mathrm{T}}{\mathrm{\rho }}\left(\frac{1}{\mathrm{r}}-\frac{1}{\mathrm{R}}\right)}$

3. $\sqrt{\frac{4\mathrm{T}}{\mathrm{\rho }}\left(\frac{1}{\mathrm{r}}-\frac{1}{\mathrm{R}}\right)}$

4. $\sqrt{\frac{6\mathrm{T}}{\mathrm{\rho }}\left(\frac{1}{\mathrm{r}}-\frac{1}{\mathrm{R}}\right)}$

 

The intensive property among the following is

1. energy

2. volume

3. entropy

4. temperature

If the work done in blowing a soap bubbie of volume V is W, then the work done in blowing a soap bubble of volume 2V will be

1. W

2. 2W

3. $\sqrt{2}$W

4. W (4)^1/3

A closed rectangular tank is completely filled with water and is accelerated horizontally with an acceleration towards right. Pressure is

(i) maximum at, and (ii) minimum at

1. (i) B (ii) D

2. (i) C (ii) D

3. (i) B (ii) C

4. (i) B (ii) A

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. $\frac{\sqrt{3}\mathrm{H}}{2}$

3. $\sqrt{3}H$

4. $\frac{3H}{4}$

The material of a wire has density of 1.4 gm/$c{m}^3$.   If it is not wetted by a liquid of surface tension 44 dyne/cm then the maximum radius of the wire which can float on the surface of liquid is

1. $\frac{1}{7}cm$

2. $\frac{5}{7}cm$

3. $\frac{5}{14}cm$

4. $\frac{2}{7}cm$

Sudden fail of atmospheric pressure by a large amount indicates

(1) storm

(2) rain

(3) fair weather.

(4) cold wave.

Two equal drops of water are falling through air with a steady velocity v. If the drops coalesce, the new velocity will be

(1) 2v

(2) $\sqrt{2}$v

(3) 2^2/3v

(4) $\frac{v}{\sqrt{2}}$

A body of density d₁ is counter poised by Mg of weights of density d₂ in air of density d. Then the true mass of the body is

(1) M

(2) $\mathrm{M}\left(1-\frac{\mathrm{d}}{{\mathrm{d}}_2}\right)$

(3) $M\left(1-\frac{d}{d_1}\right)$

(4) $\frac{M\left(1-\frac{d}{d_2}\right)}{\left(1-\frac{d}{d_1}\right)}$

A tank filled with water has two taps to exhaust and pour. A hollow spherical ball is half submerged in water. Through one tap, water is taken out and through another tap, a liquid of density double the density of water is poured in tank such that volume of liquid in tank remains constant. Sphere will

1. go down

2. go up

3. maintain same height

4. sink to bottom