Question

A small sphere of volume V falling in a viscous fluid acquires a terminal velocity vt. The terminal velocity of a sphere of volume 8 V of the same material and falling in the same fluid will be   

Solution

Correct option is

 

We know that  

         

Where 

              

Now 

         

Therefore, 

         . Thus 

         

Terminal velocity of the sphere of volume 8 V will be 

        

             

SIMILAR QUESTIONS

Q1

A glass plate (of negligible mass and thickness) is held against the end of a tube and pushed 10 cm under the surface of water. When released, the plate does not fall off. What depth of kerosene (relative density 0.8) must be poured into tube so that the plate just falls off?  

Q2

Water rises to a height of 13.6 cm in a capillary tube dipped in water. When the same tube is dipped in mercury, it is depressed by  cm. The angle of contact for water is zero and that for mercury 135o. The relative density of mercury is 13.6. The ratio of the surface tensions of mercury and water is   

Q3

Two blocks A and B are made of different kinds of wood. Block A floats in water with  of its above the surface water. Block B floats in water with  of its volume below the surface of water. The ratio of the densities of A and B is     

Q4

The pressures inside two soap bubbles are 1.002 and 1.004 atmospheres. Their respective volumes are in the ratio of

Q5

If W is the amount of work done in blowing a bubble of volume, V, what will be the amount of work done to blow a bubble of volume 8 V 

Q6

Water is flowing through a tube of radius r with a speed v. If this tube is joined to another tube of radius r/2, what is the speed of water in the second tube?

Q7

Equal masses of two substances of densities  are mixed together. The density of the mixture would be

Q8

Equal volumes of two substances of densities  are mixed together. The density of the mixture would be

Q9

A capillary tube of radius is immersed in water and water rises in it to a height h. The mass of water in the capillary tube is 5 g. Another capillary tube of radius 2r is immersed in water in water. The mass of water that will rise in this tube is  

Q10

A cubical vessel of height 1m is full of water. The work done in pumping water out of the vessel is