9303753286127016 The velocity of light (c), acceleration due to gravity (g), and atmospheric pressure (p) are chosen a fundamental units, then the dimensions of length will be

The velocity of light (c), acceleration due to gravity (g), and atmospheric pressure (p) are chosen a fundamental units, then the dimensions of length will be

 Given: Velocity of light=C

Acceleration due to gravity – g

Pressure -P

Let ‘L’ be the length.

Let’s assume, L = CxgyPz …eq i)

Now putting all the values in above equation, [M0L1T0] = [M0L1T−1]x [M0L1T−2]y [M1L−1T−2]z

⇒ [M0L1T0] = [MzLx+y−zT−x−2y−2z]

Applying the principle of homogeneity, Comparing the powers of M, z=0

Compare the powers of L, x+y−z=1 ( As z=0)

⇒ x + y =1

⇒ x = 1−y …eq ii)

Compare the powers of T, −x−2y−2z=0 ( As z=0)

⇒ −x−2y=0 …eq iii)

Put the value of eq ii) in above equation, we get ⇒ −(1−y)−2y = 0

⇒ y = −1

Putting the value of y in eq ii),

we get ⇒ x = 2

Now, put the values of x, y and z in eq i)

Therefore, the dimensions of length will be: L = C2g−1P0

⇒ L=C2/g

Balkishan Agrawal

At the helm of GMS Learning is Principal Balkishan Agrawal, a dedicated and experienced educationist. Under his able guidance, our school has flourished academically and has achieved remarkable milestones in various fields. Principal Agrawal’s vision for the school is centered on providing a nurturing environment where every student can thrive, learn, and grow.

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