Question

Find the dimensions of the following quantities

(i) Angle

(ii) Density

(iii) Kinetic energy

(iv) Gravitational constant

(v) Permeability​

Answer 1

Answer:

ANGLE:Angle is defined as the ratio of length of arc to radius. Substituting in the above formula we get, Dimensional formula of Angle = M0L0T0. We can also say Angle is dimensionless quantity.

DENSITY:The formula for density is d = M/V, where d is density, M is mass, and V is volume. Density is commonly expressed in units of grams per cubic centimetre. For example, the density of water is 1 gram per cubic centimetre, and Earth's density is 5.51 grams per cubic centimetre.

KINETIC ENERGY:Kinetic energy is one of the types of energy and it is defined as the energy in an object due to its virtue of motion. The dimension of kinetic energy will be the same as that of energy. Therefore, kinetic energy is measured in Joules (SI unit of energy) and its dimensional formula will be [M1L2T−2].

GRAVITATIONAL CONSTANT:Derivation. Or, G = [M1 L1 T-2] × [L]2 × [M]-2 = [M-1 L3 T-2]. Therefore, the gravitational constant is dimensionally represented as M-1 L3 T-2.

PERMEABILITY:Therefore, the magnetic permeability is dimensionally represented as [M1 L1 T-2 I-2].