Two bodies are in equilibrium when suspended in water from the arms of a balance. The mass of one body is \(36~\text g\) and its density is \(9~\text{g/cm}^3.\) If the mass of the other is \(48~\text g,\) its density in \((\text{g/cm}^3)\) will be:
1. \(\frac{4}{3}\)
2. \(\frac{3}{2}\)
3. \(3\)
4. \(5\)

An inverted bell lying at the bottom of a lake 47.6 m deep has 50 cm³ of air trapped in it. The bell is brought to the surface of the lake. The volume of the trapped air will be (atmospheric pressure = 70 cm of Hg and density of Hg = 13.6 g/cm³) 
(1) 350 cm³                               

(2) 300 cm³

(3) 250 cm³                               

(4) 22 cm³

A siphon in use is demonstrated in the following figure. The density of the liquid flowing in siphon is 1.5 gm/cc. The pressure difference between the point P and S will be

(1) ${10}^5 \mathrm{N}/\mathrm{m}$                                 

(2) $2\times {10}^5 \mathrm{N}/\mathrm{m}$

(3) Zero                                       

(4) Infinity 

The height of a mercury barometer is 75 cm at sea level and 50 cm at the top of a hill. Ratio of density of mercury to that of air is ${10}^4$. The height of the hill is
(1) 250 m                             

(2) 2.5 km

(3) 1.25 km                           

(4) 750 m

Equal masses of water and a liquid of relative density \(2\) are mixed together, then the mixture has a density of:
1. \(\dfrac{2}{3}\)

2. \(\dfrac{4}{3}\)

3. \(\dfrac{3}{2}\)

4. \(3\)

A body of density ${\mathrm{d}}_1$ is counterpoised by Mg of weights of density ${\mathrm{d}}_2$ 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%. The barometric height of mercury
(1) Increases by 2%

(2) Decreases by 2%

(3) Remains unchanged

(4) Sometimes increases and sometimes decreases

A barometer kept in a stationary elevator reads 76 cm. If the elevator starts accelerating up, the reading will be
(1) Zero                                       

(2) Equal to 76 cm

(3) More than 76 cm                     

(4) Less than 76 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 vertical \(\mathrm{U}\)-tube of uniform inner cross-section contains mercury in both its arms. A glycerin (density\(=1.3\) g/cm³) column of length \(10\) cm is introduced into one of its arms. Oil of density \(0.8\) g/cm³  is poured into the other arm until the upper surfaces of the oil and glycerin are at the same horizontal level. The length of the oil column is:
(density of mercury \(=13.6\) g/cm³)
                       
1. \(10.4\) cm
2. \(8.2\) cm
3. \(7.2\) cm
4. \(9.6\) cm