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Write the dimensional formulae for the following quantities. 1. Gravitational constant 2. Surface Tension

Write the dimensional formulae for the following quantities.
1. Gravitational constant 2. Surface Tension

Grade:upto college level

1 Answers

Apoorva Arora IIT Roorkee
askIITians Faculty 181 Points
6 years ago
F refers to Force, with a unit of Newton (kgm/s^2)

m1 refers to mass 1, with a unit of kg.
m2 refers to mass 2, with a unit of kg.
R^2 refers to distance of two masses (squared), with a unit of m*m = m^2

Now let's make an equation to G:

F = G m1 m2 /R^2
G = F R^2 /(m1 m2)
now input the units.
G = kgm/s^2 * m^2 / (kg * kg)
G = kgm^3/s^2 / kg^2
G = m^3/s^2 kg^2
G = kg^-2 m^3 s^-2

Now that the dimension for the unit kilogram (kg) is M], dimension for the unit meter (m) is [L], and the dimension for the unit second (s) is [T], so:

kg^-2 m^3 s^-2 --> [M]^-2 [L]^3 [T]^-2

Surface Tension is defined as force per unit length. The formula is
Surface Tension= Force/Length
Dimensional Formula of Force = M1L1T-2
Divide it by Length L1
So Dimensional Formula of Surface Tension = M1L0T-2


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