Question

1.
If force acting on a particle depends on the x-coordinates as F = ax + bx^2, find the dimensions of 'a'
and 'b'


pls answer plsss..​

Answer 1

Answer:

hope my answer helps you.........

Answer 2

Concept:

• Dimensional analysis
• Fundamental physical quantities
• Expressing physical quantities in dimensions of the fundamental physical quantities

Given:

• F = ax + bx²
• Dimensions of F = [MLT⁻²]
• x is the displacement
• Dimension of x = [L]

Find:

• The dimensions of a
• The dimensions of b

Solution:

The dimension of ax has to be the same as the dimensions of Force

Let the dimension of a be z

[MLT⁻²] = z [L]

z = [MLT⁻²]/ [L]

z = [MT⁻²]

The dimension of a = [MT⁻²]

Let the dimension of b be p

[MLT⁻²] = z [L]²

z = [MLT⁻²]/ [L]²

z = [ML⁻¹T⁻²]

The dimension of b = [ML⁻¹T⁻²]

The dimensions of a and b are [MT⁻²] and [ML⁻¹T⁻²] respectively.

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