Question

Find the dimension of a/b in the equation p=a-t2/bx where p is pressure,x is distance and t is time.

Answer 1

P = a
So a = force ÷ area
A = MLT-2 ÷ L2
A = ML-1 T-2

P = T2 ÷ BX
ML-1T-2 = T2 ÷ B L
ML-1 T-2 × L ÷ T2 = B
MT-4 = B


A÷ B = ML-1 T-2 ÷ MT-4
A ÷ B = L-1 T 2



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Answer 2

The dimension of a/b is [a/b] = [M¹T⁻²]

Given,

An equation p = (a-t²)/bx, where p is pressure, x is distance, and t is time.

To Find,

The dimension of a/b.

Solution,

The dimensions of pressure is [p] = M L⁻¹ T⁻².

Now, the given equation is

p = (a-t²)/bx

So, the dimensions of a will be equal to the dimensions of t²

[a} = T²

Now,

[b] = [a-t²]/[p][x]

[b] = [T²]/[M¹L⁻¹T⁻²][L¹]

[b] = [M⁻¹L°T⁴]

Now, the dimensions of a/b will be

[a/b] = [a]/[b] = [T²]/[M⁻¹L°T⁴]

[a/b] = [M¹T⁻²]

Hence, the dimension of a/b is [a/b] = [M¹T⁻²]

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