The density of a material in CGS system of units is 4 g/cm³ . . .

Question : The density of a material in CGS system of units is 4 g/cm³. In a system of units in which unit of length is 10 cm and unit of mass is 100 g, the value of density of material will be

a) 400

b) 0.04

c) 0.4

d) 40

Doubt by Sanya

Solution : 

Dimensional Formula of Density 

[M¹L^-3T⁰]
a=1, b=-3, c=0

n₁=4

M₁=1g

L₁=1cm

n₂=?

M₁=100g
L₁=10cm

n₂=n₁[M₁/M₂]^a[L₁/L₂]^b[T₁/T₂]^c

n₂=4[1/100]¹[1/10]^-3[T₁/T₂]⁰
n₂=4[1/100][10]3×1

n₂=4[1000/100]
n₂=4×10
n₂=40

Hence, d) 40 will be the correct option.