Advertisements
Advertisements
प्रश्न
A ferry boat has internal volume 1 m3 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?
Advertisements
उत्तर
Internal volume, V = 1 m3 = External volume of the ferry boat
Density of water, \[\rho_w\] = 103 kg/m3
As the weight of the boat is balanced by the buoyant force, we have:
\[\text{mg} = V_1 \times \rho_w \times g\]
\[ \Rightarrow 50 = V_1 \times {10}^3 \]
\[ \Rightarrow V_1 = \frac{5}{100} = 0 . 05 \text{ m}^3\]
(b) Let V2 be the volume of the boat filled with water before water starts coming in from the side.
\[\therefore \text {mg + V}_2 \rho_\text{w} \times \text{g = V} \times \rho_\text{w} \times g [\text{ V is the volume of the water displaced by the boat }. ]\]
\[ \Rightarrow 50 + V_2 \times {10}^3 = 1 \times {10}^3 \]
\[ \Rightarrow V_2 = \frac{{10}^3 - 50}{{10}^3}\]
\[ = \frac{950}{1000} = 0 . 95 \text{ m}^3 \]
Fraction of the boat's volume filled with water\[ = \frac{19}{20}\]
APPEARS IN
संबंधित प्रश्न
Mercury has an angle of contact equal to 140° with soda lime glass. A narrow tube of radius 1.00 mm made of this glass is dipped in a trough containing mercury. By what amount does the mercury dip down in the tube relative to the liquid surface outside? Surface tension of mercury at the temperature of the experiment is 0.465 N m–1. Density of mercury = 13.6 × 103 kg m–3
State any two characteristics of the angle of contact
If more air is pushed in a soap bubble, the pressure in it
The rise of a liquid in a capillary tube depends on
(a) the material
(b) the length
(c) the outer radius
(d) the inner radius of the tube
A barometer is constructed with its tube having radius 1.0 mm. Assume that the surface of mercury in the tube is spherical in shape. If the atmospheric pressure is equal to 76 cm of mercury, what will be the height raised in the barometer tube? The contact angle of mercury with glass = 135° and surface tension of mercury = 0.465 N m−1. Density of mercury = 13600 kg m−3.
A drop of mercury of radius 2 mm is split into 8 identical droplets. Find the increase in surface energy. Surface tension of mercury = 0.465 J m−2.
A capillary tube of radius 1 mm is kept vertical with the lower end in water. (a) Find the height of water raised in the capillary. (b) If the length of the capillary tube is half the answer of part , find the angle θ made by the water surface in the capillary with the wall.
A solid sphere of radius 5 cm floats in water. If a maximum load of 0.1 kg can be put on it without wetting the load, find the specific gravity of the material of the sphere.
Explain the capillary action.
Derive an expression for capillary rise for a liquid having a concave meniscus.
Define surface tension.
What will be the shape of the liquid meniscus for the obtuse angle of contact?
A certain number of spherical drops of a liquid of radius R coalesce to form a single drop of radius R and volume V. If T is the surface tension of the liquid, then
A drop of oil placed on the surface of water spreads out. But a drop of water place on oil contracts to a spherical shape. Why?
A spherical soap bubble A of radius 2 cm is formed inside another bubble B of radius 4 cm. Show that the radius of a single soap bubble which maintains the same pressure difference as inside the smaller and outside the larger soap bubble is lesser than the radius of both soap bubbles A and B.
Why is raindrop spherical in nature?
A coaxial cylinder made of glass is immersed in liquid of surface tension ' S'. Radius of inner and outer surface of cylinder are R1 and R2 respectively. Height till which liquid will rise is (Density of liquid is p):
A soap film of surface tension 3 × 10-2 formed in a rectangular frame can support a straw as shown in Fig. If g = 10 ms-12, the mass of the straw is ______.
Define angle of contact.
