Question

A boat of area 10 m2 floating on the surface of a river is made to move horizontally with a speed of 2 m/s by applying a tangential force. If the river is 1 m deep and the water in contact with the bed is stationary, find the tangential force needed to keep the boat moving with same velocity. Viscosity of water is 0.01 poise.   

Solution

Correct option is

0.02 N

 

A velocity changes from a 2 m/s at the surface to zero at the bed which is at a depth of 1 m,  

            

Now from Newton’s law of viscous force, 

      

            .

So to keep the boat moving at same velocity, force equal to viscous force, i.e., 0.02 N must be applied.

SIMILAR QUESTIONS

Q1

A drop of mercury has a radius of 3.00 mm at room temperature. The surface tension of mercury at that temperature is 0.465 Nm–1. Find excess pressure inside the drop and the total pressure inside the drop. The atmospheric pressure is .

Q2

What is the excess pressure in a soap bubble of radius 5.00 mm at 20oC? The surface tension of soap solution at 20oC is .

Q3

 

If an air bubble of same radius be formed at a depth of 40.0 cm in a soap solution (relative density 1.20), then what will be the pressure inside the air bubble?

Q4

Two spherical soap bubbles of different radii coalesce. If V is the consequent change in volume of the contained air, and S the change in the total surface area, then show that 3PV + 4ST = 0, where T is surface tension of the soap solution.       

Q5

The limbs of a manometer consist of uniform capillary tubes of radii . Find out the pressure difference if the level of the liquid (density 103 kg/m3, surface tension ) in the narrower tube stands 0.2 m above that in the broader tube. 

Q6

Two separate air bubble (radii 0.002 m and 0.004 m) formed of the same liquid (surface tension 0.07 N/m) come together to form a double. Find the radius and the sense of curvature of two internal film surface common to both the bubbles.  

Q7

Two capillary tubes of diameters 5.0 mm and 4.0 mm are held vertically inside water one by one. How much high the water will rise in each tube? (g = 9.8 N kg–1, surface tension of water )

Q8

Water rises in a capillary tube to a height 2.0 cm. In an another capillary whose radius is one-third of it, how much the water will rise? If the first capillary is inclined at an angle of 60o with the vertical then what will be the position of water in the tube?   

Q9

A cylindrical tank 1 m in radius rests on a platform 5 m high. Initially the tank is filled with water upto a height of 5 m. a plug whose area is 10–4 m2is removed from an orifice on the side of the tank at the bottom. Calculate time taken to empty the tank to half its original value.  

Q10

The velocity of water in a river is 18 km/hr at the surface. If the river is 5 m deep, find the shearing stress between the horizontal layers of water. The viscosity of water is 10–3 poiseuille.