Facts that Matter
The force is along the line joining the centres of two objects.
Let two objects A and B of masses M and m lie at a distance of d from each other as shown in the figure.
Let F be the force of attraction between two objects. According to the universal law of gravitation
S.I. unit of G = Nm2/kg2
Value of G = 6.673 × 10−11 Nm2/kg2 (Found by Henry Cavendish)
F = G(Mm/d2) (from Universal law of gravitation) ...(iii)
From (ii) and (iii)
∴ mg = G(Mm/d2)
∴ g= GM/d2
M = Mass of the earth
d = Distance between the object and the earth
G = Gravitational constant If the object is placed on the earth then
d = R (R = radius of the earth)
Earth is not a sphere, it is flattened at poles.
Hence Rp − Radius at pole and Re − Radius at equator
∴ The value of ‘g’ is more at poles = (9.9 m/s2) and less at equator = (9.8 m/s2)
Calculation of value of g
G = 6.67 x 10-11 Nm2/kg2
M = 6 × 1024 kg (Mass of the earth)
R = 6.4 × 106 m
On substituting the given values
Motion of objects under the influence of gravity ‘g’ does not depend on the mass of the body. All objects small, big, heavy, light, hollow or solid fall at same rate.
W = m × g
The weight of an object can change from one place to the other, from one planet to the other.
Weight of an object on moon is given by the formula
Wm = weight of an object on moon
Mm = Mass of the moon = 7.36 x 1022
Rm = radius of the moon = 1.74 x 106
G = 6.67 x 10-11 Nm2/kg2
Wm = 1.474 × 1010 G × m
and We = 1.474 × 1011 G × m
∴ Weight of an object on moon = (1/6) th the weight of an object on the earth.
Pressure = thrust / area , S.I unit = N/m2 = Pascal (pa)
The magnitude of the buoyant force depends on the density of the fluid.
A − Wooden block
B1 − Beaker with tap water
B2 − Beaker with salty water
The buoyant force exerted in B2 is more as compared to B1. It is because the density of B2 water is more.
The object may float, sink or remain half submerged and half above water, the density of the fluid and object decides this.
– If the density of object is less than the fluid, then it will float on the liquid.
– If the density of object is more than the fluid, then it will sink in the liquid.
– If the density of object is same as the density of fluid, then it will half float and half sink.
(i) Used in designing ships and submarines,
(ii) In lactometers to find purity of milk.
(iii) In hydrometer to determine density of liquid.
Relative density = density of substance / density of water
It has no unit.