Mass of the girl = 60 kg
Diameter of the heel (d) = 1 cm = 0.01 m
Radius of the heel (r) = \(\frac {d}{2} = \frac {0.01}{2}\)
r = 0.005 m
Area of the heel = πr² = π x (0.005)²
= 7.85 x 10^-5m²
Force exerted by the heel on the floor
F = mg
F = 60 x 9.8 = 588 N
Pressure exerted by the heel on the floor
P = \(\frac {F}{A}\)
F = \(\frac {588}{7.85 \times {10}^{-5}}\) = 7.490 x 10⁶ N/m²
The pressure exerted by heel on the horizontal area = 7.5 x 10⁶ pascals.

Volume of the packet V = 300 cm³
mass of the packet M = 500 g
Density of the packet p = \(\frac {M}{V}\)
= \(\frac {500}{300}\) = 1.666 gcm^-3
= 1.67 gcm^-3
As the density of the packet is greater than that of water, it will sink in water.
Mass of water displaced by the packet is equal to the volume of the packet times the density of water.
∴ m_w = ρ_w x v
= 1 gcm^-3 x 300 cm³ = 300 grams
∴ Mass of the water displaced = 300 grams.

In deep sea, the pressure of water is more than twice the atmospheric pressure, parts of our body, especially blood vessels and soft tissues cannot withstand such high pressure. Hence scuba divers always wear special suits and equipment to protect them.

Archimedes principle states that a body immersed in a fluid experiences a vertical upward buoyant force equal to the weight of the fluid it displaces.

The upward force acting on an object immersed in a liquid is known as upthrust or buoyant force.
It depends on
i) volume of the object immersed in the liquid.
ii) Density of the liquid.

a) Buoyant force depends upon volume of solid and density of water. Since, saturated salt solution have higher density than water, cube will experience a greater buoyant force.
If each side of the cube is reduced to 4cm, the volume of the cube will become less, so buoyant force will be less than as compared to the first case for water.
b) The buoyant force acting on the ball
F = volume of the ball x density of water x acceleration due to gravity
Volume of the ball = \(\frac {Mass of the ball}{Density of the ball}\)
= \(\frac {4 kg}{4000 kg {m}^{3}}\)
= 0.001 m³
The buoyant force acting on the ball
F = 0.001 m³ x 1000kg/m³ x 10m/s².
F = 10 N

1. The instrument used to measure the purity of milk is Lactometer .
2. Lactometer works on the principle of gravity of milk.
Working:
1. The lactometer consists of a long graduated test tube with a cylindrical bulb with the graduation ranging from 15 at the top to 45 at the bottom. The test tube is filled with air. This air chamber causes the instrument to float.
2. The spherical bulb is filled with mercury to cause the lactometer to sink up to the proper level and to float in an upright position in the milk.
3. Inside the lactometer there may be a thermometer extending from the bulb up into the upper part of the test tube where the scale is located.
4. The correct lactometer reading is obtained only at the temperature of 60^oC.
5. A lactometer measures the cream content of milk. More the cream, lower the lactometer floats in the milk. The average reading of normal milk is 32.
6. Lactometers are used highly at milk processing units and at the dairies.