There is a hole in the bottom of a tank having water. If the total pressure at the bottom is \(3\) atm \((1~\text{atm}=10^5~\text{N}/\text{m}^2),\) then the velocity of water flowing from the hole is:
1. \(\sqrt{400}~~\text{m/s}\)
2. \(\sqrt{600}~~\text{m/s}\)
3. \(\sqrt{60}~~\text{m/s}\)
4. none of these

A spherical ball of radius \(r\) is falling in a viscous fluid of viscosity \(\eta\) with a velocity \(v.\) The retarding viscous force acting on the spherical ball is:

The pans of a physical balance are in equilibrium. If Air is blown under the right-hand pan then the right-hand pan will:

A tank is filled with water up to a height \(H.\) The water is allowed to come out of a hole \(P\) in one of the walls at a depth \(D\) below the surface of the water. The horizontal distance \({x}\) in terms of \(H\) and \({D}\) is:
    
1. \(x = \sqrt{D\left(H-D\right)}\)
2. \(x = \sqrt{\frac{D \left(H - D \right)}{2}}\)
3. \(x = 2 \sqrt{D \left(H-D\right)}\)
4. \(x = 4 \sqrt{D \left(H-D\right)}\)

If the excess pressure inside a soap bubble is balanced by an oil column of height of \(2~\text{mm},\) then the surface tension of the soap solution will be:
(the radius of the soap bubble, \(r=1~\text{cm}\) and density of oil, \(d=0.8~\text{gm/cm}^3\) )
1. \(3.9~\text {N/m}\) 
2. $\mathrm{}$\(3.9\times 10^{-2}~\text{N/m}\)$\mathrm{}$
3. $\mathrm{}$\(3.9\times 10^{-3}~\text{N/m}\)$\mathrm{}$
4. \(3.9​​​​~\text{dyne/m}\) 

If the surface tension of water is \(0.06~\text{N/m}^2,\) then the capillary rise in a tube of diameter \(1~\text{mm}\) is:
\((\theta = 0^{\circ})\)

1. \(1.22~\text {m}\)
2. \(2.44~\text {cm}\)
3. \(3.12~\text {cm}\)
4. \(3.86~\text {cm}\) 

The following figure shows the flow of liquid through a horizontal pipe. Three tubes \(A,\) \(B\) and \(C\) are connected to the pipe. The radii of the tubes  \(A,\) \(B\) and \(C\) at the junction are respectively \(2~\text{cm},1~\text{cm}\) and \(2~\text{cm}.\) It can be said that:

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 \(76 ~\text{cm}\)

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

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: