Question

A wooden ball of density  is released from the bottom of a tank which is filled with a liquid of density  up to a height h1. The ball rises in the liquid, emerges from its surface and attains a height h2 in air. If viscous effects are neglected, the ratio h2/h1 is   

Solution

Correct option is

 

Weight of the ball

      

Upthrust 

Therefore, the net upward force acting on the ball is  

        

Now, mass of the ball is . Therefore, upward acceleration of the ball while it is rising in the liquid is  

        

            

            

Velocity of the ball on reaching the surface of water is  

          

This is the initial upward velocity of the ball in air. If it rises to a height h2in air, we have   

             

Equating (i) and (ii), we have a h1 = g h2

  

              

              .

SIMILAR QUESTIONS

Q1

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 

Q2

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 

Q3

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?

Q4

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   

Q5

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. 

Q6

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

Q7

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?  

Q8

The time period of a simple pendulum is T. The pendulum is oscillated with its bob immersed in a liquid of density . If the density of the bob is  and viscous effect is neglected, the time period of the pendulum will be

Q9

A wooden block of mass m and density  is tied to a string; the other end of the string is fixed to the bottom of a tank. The tank is filled with a liquid of density . What is the tension in the string. 

Q10

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?