Question

A spherical small ball of density  is gently released in a liquid of density . The initial acceleration of the free fall of the ball will be

Solution

Correct option is

 

Let m be the mass of the ball and V its volume. Its mass . The weight of the ball is

         

The volume of the liquid displaced = V. If  is the density of the liquid, the weight of the liquid displaced is the upthrust U it experiences. 

          

 The net downward force acting on the body is

          

The initial acceleration is 

         

SIMILAR QUESTIONS

Q1

If the surface tension of soap solution is , What is the work done in blowing soap bubble of radius r?

Q2

The work done to break up a drop of a liquid of radius R and surface tension  into eight drops, all of the same size, is 

Q3

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

Q4

If the air bubble is formed at a depth h inside the container of soap solution of density , the total pressure inside the bubble is (here P0denotes the atmospheric pressure) 

Q5

A small drop of water of surface tension  is squeezed between two clean glass plates so that a thin layer of thickness d and area A is formed between them. If the angle of contact is zero, the force required to pull the plates apart is 

Q6

Eight drop of water, each of radius r, coalesce to form a single big drop. The energy released is used up in raising the temperature of the big drop. If is the surface tension of water and  its density and J the mechanical equivalent of heat (all expressed in SI units), the rise in the temperature of the drop is 

Q7

Water rises to a height h in a capillary tube of area of cross-section a. To what height will water rise in a capillary tube of area of cross-section 4a?

Q8

A metal sphere of volume V, having a cavity inside it, floats on water completely submerged. If the relative density of the metal is 1.5, the volume of the cavity is   

Q9

The terminal velocity of a tiny brass sphere of radius r falling in a viscous liquid is vr. What will be the terminal velocity of a brass sphere of radius 2rfalling in the same liquid. 

Q10

A cylinder has a radius r. To what height h should it be filled with water so that the thrust on its walls is equal to that on its bottom?