Question

☺Please answer this guys ✌☝

●Class 11 UNIT & DIMENSIONS

Answer 1

Heya.....^_^

Here's ur ans.⬇

c = Speed of light
Dimension formula (c) = LT^-1

h = Planck's constant
D.F (h) = ML^2T^-1

G= Newton's gravitational constant
D.F (G) = M^-1 L^3 T^-2

Dimension formula of mass = c^x h^y G^z

(In new system of unit
Assume x, y and z as there power)

M L^0 T^0 =( LT^-1)^x (ML^2T^-1) ^y (M^-1L^3T^-2)

M L^0 T^0 = M^(y-z) L^(x+2y+3z) T^(-x-y-2z)

On comparing

x + 2y + 3z = 0 ... 1st equation

y-z = 1 ... 2nd equation

-x-y-2z = 0. ... 3rd equation

From 2nd equation

y = 1+z

Substituting it in 1st equation

x + 2(1+z) + 3z = 0
x+2+5z = 0
x = -5z -2

Now. , Substituting the value of x and y in 3rd equation

-(-5z-2) - (1+z) -2z = 0
5z + 2 - 1- z -2z = 0
2z +1 = 0

↪ z = -1/2
Therefore

↪ x = -5 × (-1/2 ) -2 = 1/2

↪ y = 1+(-1/2 )= 1/2

Hence , Dimension formula of mass ⬇

${c}^{2} {h}^{ 1 \div 2} g {}^{ - 1 \div 2}$
Similarly , u can find it for length and time

Hope it helps