The height of a mercury barometer is \(75 ~\text{cm}\) at sea level and \(50 ~\text{cm}\) at the top of a hill. The ratio of the density of mercury to that of air is \(10^4.\) The height of the hill is:

1.	\(250 ~\text m\)	2.	\(2.5 ~\text {km}\)
3.	\(1.25 ~\text {km}\)	4.	\(750 ~\text m\)

A body of density d₁ is counterpoised 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. $\mathrm{M}\left(1-\frac{\mathrm{d}}{{\mathrm{d}}_1}\right)$                       

4. $\frac{\mathrm{M}(1-\mathrm{d}/{\mathrm{d}}_2)}{(1-\mathrm{d}/{\mathrm{d}}_1)}$

The value of g at a place decreases by 2%. Then, the barometric height of mercury:

A barometer kept in a stationary elevator reads \(76 ~\text{cm}.\) If the elevator starts accelerating up, the reading will be:
1. zero
2. equal to \(76 ~\text{cm}\)
3. more than \(76 ~\text{cm}\)
4. less than \(76 ~\text{cm}\)

A closed rectangular tank is completely filled with water and is accelerated horizontally with an acceleration a 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 beaker containing a liquid is kept inside a big closed jar. If the air inside the jar is continuously pumped out, the pressure in the liquid near the bottom of the beaker will

1. Increase

2. Decrease

3. Remain constant

4. First decrease and then increase

A given shaped glass tube having uniform cross section is filled with water and is mounted on a rotatable shaft as shown in figure. If the tube is rotated with a constant angular velocity $\mathrm{\omega }$ then

1. Water levels in both sections A and B go up

2. Water level in Section A goes up and that in B comes down

3. Water level in Section A comes down and that in B it goes up

4. Water levels remains same in both sections

An ice berg of density 900 Kg/${\mathrm{m}}^3$ is floating in water of density 1000 Kg/${\mathrm{m}}^3$. The percentage of volume of ice-cube outside the water is 

1. 20%                                     

2. 35%

3. 10%                                       

4. 25%

A log of wood of mass 120 Kg floats in water. The weight that can be put on the raft to make it just sink, should be (density of wood = 600 Kg/${\mathrm{m}}^3$) 

1. 80 Kg                                                 

2. 50 Kg

3. 60 Kg                                                 

4. 30 Kg

A hemispherical bowl just floats without sinking in a liquid of density $1.2\times {10}^3 \mathrm{kg}/{\mathrm{m}}^3$. If outer diameter and the density of the bowl are 1 m and $2\times {10}^4 \mathrm{kg}/{\mathrm{m}}^3$ respectively, then the inner diameter of the bowl will be 

1. 0.94 m                           

2. 0.97 m

3. 0.98 m                           

4. 0.99 m