Question

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     

Solution

Correct option is

9 : 8

 

Let V1 be the volume of block A and  is density. Then, from the principle of flotation, we have

          

  

where  is the density of water. Simplify for block B we have

          

  

  

              .

SIMILAR QUESTIONS

Q1

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   

Q2

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. 

Q3

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

Q4

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?  

Q5

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

Q6

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. 

Q7

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   

Q8

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?  

Q9

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   

Q10

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