Question

Displacement(s) of a body in a time 't' is given by s=at^2+bt. Find dimension of a&b

Answer 1

Dimension of a is L/T^2

Dimension of b is L/T

Answer 2

The dimensions of a and b are [LT⁻³] and [LT⁻²] respectively.

Given,

The displacement of the body is given as s = at²+bt.

To Find,

The dimensions of a and b.

Solution,

The dimensional formula of displacement(s) is [LT⁻¹].

Now, the given expression is

s = at²+bt

So,

The dimensions of s will be the same as that of at² and bt.

[LT⁻¹] = a[T²]

a = [LT⁻³]

Now,

The dimensional formula of b will be

[LT⁻¹] = b[T¹]

b = [LT⁻²]

Hence, the dimensions of a and b are [LT⁻³] and [LT⁻²] respectively.

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