If there were a smaller gravitational effect, which of the following forces do you think would alter in some respect?

1.  Viscous forces                   

2.  Archimedes uplift

3.  Electrostatic force              

4.  None of the above

Two non-mixing liquids of densities and \(n 𝜌 (n>1)\) are put in a container. The height of each liquid is \(h.\) A solid cylinder floats with its axis vertical and length \(pL  (𝑝 < 1)\) in the denser liquid. The density of the cylinder is \(d.\) The density \(d\) is equal to:
1. \({[2+(n+1)p}] 𝜌\)
2. \([{2+(n-1)p}] 𝜌\)
3. \([{1+(n-1)p}] 𝜌\)
4. \([{1+(n+1)p}] 𝜌\)

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. \(5\)

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

An iceberg of density \(900 ~\text{kg/m}^ 3\)${\mathrm{}}^{}$ is floating in the water of density \(1000 ~\text{kg/m}^ 3.\) The percentage of the 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 the outer diameter and the density of the material 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

A concrete sphere of radius R has a cavity of radius r which is packed with sawdust. The specific gravities of concrete and sawdust are respectively 2.4 and 0.3. For this sphere to float with its entire volume submerged underwater, the ratio of mass of concrete to mass of sawdust will be:

A metallic block of density 5 gm ${\mathrm{cm}}^{-3}$ and having dimensions 5 cm × 5 cm × 5 cm is weighed in water. Its apparent weight will be

1. 5 × 5 × 5 × 5 gf                           

2. 4 × 4 × 4 × 4 gf

3. 5 × 4 × 4 × 4 gf                           

4. 4 × 5 × 5 × 5 gf

A cubical block is floating in a liquid with half of its volume immersed in the liquid. When the whole system accelerates upwards with acceleration of g/3, the fraction of volume immersed in the liquid will be

1. $\frac{1}{2}$                                 

2. $\frac{3}{8}$

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

4. $\frac{3}{4}$