All the values and formulas from lesson gravitation
Universal Law of Gravitation All the formulas associated with it is given below.
F∝M⋅m
F∝1/d^2
F∝M⋅md^2
⇒F=(G⋅M⋅m)/d2
F×d^2=G⋅M⋅m
⇒G=F.d^2/(M⋅m)
SI Unit of G
The SI unit of G Nm^2kg^-2
The accepted value of G is 6.673×10−11Nm^2 kg^−2
Expression for acceleration due to gravitation g
according to Newton’s Second Law of Motion which states that Force is the product of mass and acceleration,
F = m x g
⇒g=GM/d^2
When object is near the surface of earth
g=GM/R^2
Calculation of value of g
We know that,
The accepted value of G is 6.673×10−11Nm^2kg^−2
The mass of earth, M=6×10^24
The radius of earth, R=6.4×10^6m
⇒g=9.8 m s^−2
Motion of an object under the influence of gravitational force of earth
The expression for ‘g’ is written as g=GM/R^2
Since, the value of ‘g’ does not depend upon the mass or distance of an object, therefore, all objects fall over the earth with the same rate.
The equations for motion are as follows:
v=u+at
s=ut+1/2at^2
v^2=u^2+2as
Therefore, the equations of motion are also applied to calculate the velocity, distance, etc by replacing ‘a’ by ‘g’. After substituting ‘g’ at the place of ‘a’ we get above equations as follows:
v=u+gt
s=ut+1/2 x gt^2
v^2=u^2+2gs
In the calculation; initial velocity (u), final velocity (v), time taken (t), or distance covered (s), the value of ‘g’ is taken as positive in the case of object moving towards earth and taken as negative in the case of object is thrown in opposite direction of earth.
Unit of weight is ‘newton (N)’.
The Mass of Earth = 5.98 x 10^ 24 kg
Radius of earth = 6.37 x 10^6 m
Mass of moon = 7.36 x 10^22 kg
Radius of moon = 1.76 x 10^6 m
Weight of the object on earth We = m x g
Weight of the object on moon Wm=m×gm(here m is subscript it signifies on moon)
, Weight of an object on moon / Weight of an object on earth = 1/6
Or, Weight of an object on the moon = 1/6th of the weight of the object on earth.
Wm/We==1/6.030≈1/6
Pressure=Force/Area
Or, Pressure=Thrust/Area
Or, p=F/A
SI unit of Pressure
p=N/m^2
or Nm^−2
Or, 1 pascal = N m^ – 2
Density(ρ)=Mass/Volume
Density(ρ)=mV
⇒ρ=m/V
ρ=kgm^3
Therefore, SI unit of density (ρ) is kgm−3
Relative density
=Density of substance/Density of water
Universal Law of Gravitation All the formulas associated with it is given below.
F∝M⋅m
F∝1/d^2
F∝M⋅md^2
⇒F=(G⋅M⋅m)/d2
F×d^2=G⋅M⋅m
⇒G=F.d^2/(M⋅m)
SI Unit of G
The SI unit of G Nm^2kg^-2
The accepted value of G is 6.673×10−11Nm^2 kg^−2
Expression for acceleration due to gravitation g
according to Newton’s Second Law of Motion which states that Force is the product of mass and acceleration,
F = m x g
⇒g=GM/d^2
When object is near the surface of earth
g=GM/R^2
Calculation of value of g
We know that,
The accepted value of G is 6.673×10−11Nm^2kg^−2
The mass of earth, M=6×10^24
The radius of earth, R=6.4×10^6m
⇒g=9.8 m s^−2
Motion of an object under the influence of gravitational force of earth
The expression for ‘g’ is written as g=GM/R^2
Since, the value of ‘g’ does not depend upon the mass or distance of an object, therefore, all objects fall over the earth with the same rate.
The equations for motion are as follows:
v=u+at
s=ut+1/2at^2
v^2=u^2+2as
Therefore, the equations of motion are also applied to calculate the velocity, distance, etc by replacing ‘a’ by ‘g’. After substituting ‘g’ at the place of ‘a’ we get above equations as follows:
v=u+gt
s=ut+1/2 x gt^2
v^2=u^2+2gs
In the calculation; initial velocity (u), final velocity (v), time taken (t), or distance covered (s), the value of ‘g’ is taken as positive in the case of object moving towards earth and taken as negative in the case of object is thrown in opposite direction of earth.
Unit of weight is ‘newton (N)’.
The Mass of Earth = 5.98 x 10^ 24 kg
Radius of earth = 6.37 x 10^6 m
Mass of moon = 7.36 x 10^22 kg
Radius of moon = 1.76 x 10^6 m
Weight of the object on earth We = m x g
Weight of the object on moon Wm=m×gm(here m is subscript it signifies on moon)
, Weight of an object on moon / Weight of an object on earth = 1/6
Or, Weight of an object on the moon = 1/6th of the weight of the object on earth.
Wm/We==1/6.030≈1/6
Pressure=Force/Area
Or, Pressure=Thrust/Area
Or, p=F/A
SI unit of Pressure
p=N/m^2
or Nm^−2
Or, 1 pascal = N m^ – 2
Density(ρ)=Mass/Volume
Density(ρ)=mV
⇒ρ=m/V
ρ=kgm^3
Therefore, SI unit of density (ρ) is kgm−3
Relative density
=Density of substance/Density of water
