**Question #1**

For a floating body, buoyant force acts at the

(A) centroid of the floating body

(B) center of gravity of the body

(C) centroid of the fluid vertically below the body

(D) centroid of the displaced fluid

**[GATE 16 S1, 1 mark]**

**Question #2**

An inverted U-tube manometer is used to measure the pressure difference between two pipes A and B, as shown in the figure. Pipe A is carrying oil (specific gravity = 0.8) and pipe B is carrying water. The densities of air and water are 1.16 kg/m3 and 1000 kg/m ^{3}, respectively. The pressure difference between pipes A and B is __________kPa.

Acceleration due to gravity g = 10 m/s2

**[GATE 16 S1, 2 marks]**

**Question #3**

Consider a frictionless, massless and leak-proof plug blocking a rectangular hole of dimensions 2R x L at the bottom of an open tank as shown in the figure. The head of the plug has the shape of a semi-cylinder of radius R. The tank is filled with a liquid of density $\rho$ up to the tip of the plug.

The gravitational acceleration is g. Neglect the effect of the atmospheric pressure.

The force Of required to hold the plug in its position is

(A)$2\rho R^2gL(1-\frac{\pi}{4})$

(B)$2\rho R^2gL(1+\frac{\pi}{4})$

(C)$\pi R^2\rho gL$

(D)$\frac{\pi }{2}\rho R^2gL$

**[GATE 16 S2, 2 marks]**

**Question #4**

The large vessel shown in the figure contains oil and water. A body is submerged at the interface of oil and water such that 45 percent of its volume is in oil while the rest is in water. The density of the body is _________ kg/m^{3}

**[GATE 16 S2, 2 marks]**

The specific gravity of oil is 0.7 and density of water is 1000 kg/m^{3}

Acceleration due to gravity g = 10 m/s^{2}

**Question #5**

For a completely submerged body with centre of gravity ‘G’ and centre of buoyancy ‘B’, the condition of stability will be

(A) G is located below B

(B) G is located above B

(C) G and B are coincident

(D) independent of the locations of G and B

**[GATE 14 S1, 1 mark]**

**Question #6**

A spherical balloon with a diameter of 10 m, shown in the figure below is used for advertisements. The balloon is filled with helium (R _{He} = 2.08 kJ/kg.K) at ambient conditions of 15°C and 100 kPa. Assuming no disturbances due to wind, the maximum allowable weight (in newton) of balloon material and rope required to avoid the fall of the balloon ( R _{air} = 0.289 kJ/kg.K) is _______

**[GATE 14 S1, 2 marks]**