The neck and bottom of a bottle are 3 cm and 15 cm in radius respectively. If the cork is pressed with a force 12 N in the neck of the bottle, then force exerted on the bottom of the bottle is

• 30 N

• 150 N

• 300 N

• 600 N

A square wire frame of size L is dipped in a liquid. On taking out a membrane is formed. If the surface tension of liquid is T, then force acting on a frame will be

• 2T L

• 4T L

• 8T L

• 16T L

64 spherical rain drops of equal size are falling vertically through air with a terminal velocity 1.5 ms^-1 .If these drops coalesce to form a big spherical drop, then terminal velocity of big drop is

• 8 ms^-1

• 16 ms^-1

• 24 ms^-1

• 32 ms^-1

104.

The equation of a wave is y = 5 sin $\left(\frac{\mathrm{t}}{0.04}- \frac{\mathrm{x}}{4}\right)$ ; where x is in cm and t is in second. The maximum velocity of the wave will be

• 1 ms^-1

• 2 ms^-1

• 1.5 ms^-1

• 1.25 ms^-1

If there were no gravity, which of the following will not be there for a fluid?

• Viscosity

• Surface tension

• Pressure

• Archimedes' upward thrust

The cylindrical tube of a spray pump has a cross-section of 8 cm² , one end of which has 40 fine holes each of area 10^-8 m². If the liquid flows inside the tube with a speed of 0.15 m min^-1 the speed with which the liquid is ejected through the holes is

• 50 m/s

• 5 m/s

• 0.05 m/s

• 0.5 m/s

Horizontal tube of non-uniform cross-section has radii of 0.1 m and 0.05 m respectively at M and N. For a streamline flow of liquid, the rate of liquid flow is

• changing continuously with time

• greater at M than at N

• greater at N than at M

• same at M and N

If two soap bubbles of different radii are connected by a tube, then

• air flows from bigger bubble to the smaller bubble till sizes become equal

• air flows from bigger bubble to the smaller bubble till sizes are interchanged

• air flows from smaller bubble to bigger

• there is no flow of air

A soap bubble of radius r is blown up to form a bubble of radius 2r under isothermal conditions. If  T  is the surface tension of soap solution, the energy spent in the blowing

• $3 {\mathrm{\pi Tr}}^2$

• $6{\mathrm{\pi Tr}}^2$

• $12{\mathrm{\pi Tr}}^2$

• $24 {\mathrm{\pi Tr}}^2$

A hollow sphere of volume V is floating on water surface with half immersed in it. What should be the minimum volume of water poured inside the sphere so that the sphere now sinks into the water 

• $\frac{\mathrm{V}}{2}$

• $\frac{\mathrm{V}}{3}$

• $\frac{\mathrm{V}}{4}$

• V