Q. 12

# A ferry boat has internal volume 1 m^{3} and weight 50 kg. (a) Neglecting the thickness of the wood, find the fraction of the volume of the boat immersed in water. (b) If a leak develops in the bottom and water starts coming in, what fraction of the boat’s volume will be filled with water before water starts coming in from the sides?

Answer :

(a)The volume of boat immersed is equal to the weight of the boat. Here, the mass of the boat, . Let the volume of the boat be V and the density of water be .

Therefore, the buoyant force should be equal to the weight of the boat.

(b) If the water comes up from the sides, this would mean that the boat is completely immersed in water. The volume of the boat, , and

Therefore, buoyant force would be

This buoyant force is equal to the weight of the boat and the weight of water. Let the mass of water be “”.

Therefore,

The volume of water would be,

Fraction of water filled in the boat = (ANS)

Rate this question :

The weight of an empty balloon on a spring balance is W_{1}. The weight becomes W_{2} when the balloon is filled with air. Let the weight of the air itself be ω. Neglect the thickness of the balloon when it is filled with air. Also neglect the difference in the densities of air inside and outside the balloon.

A solid float in a liquid in a partially dipped position.

HC Verma - Concepts of Physics Part 1Streamline flow is more likely for liquids with

Physics - ExemplarIf water be used to construct a barometer, what would be the height of water column at standard atmospheric pressure (76 cm of mercury)?

HC Verma - Concepts of Physics Part 1Find the force exerted by the water on a 2 m^{2} plane surface of a large stone placed at the bottom of a sea 500 m deep. Does the force depend on the orientation of the surface?

Suppose the glass of the previous problem is covered by a jar and the air inside the jar is completely pumped out. (a) What will be the answers to the problem? (b) Show that the answers do not change if a glass of different shape is used provided the height, the bottom area and the volume are unchanged.

HC Verma - Concepts of Physics Part 1Water level is maintained in a cylindrical vessel up to a fixed height H. The vessel is kept on a horizontal plane. At what height above the bottom should a hole be made in the vessel so that the water stream coming out of the hole strikes the horizontal plane at the greatest distance from the vessel (figure 13-E11)?

HC Verma - Concepts of Physics Part 1