Question

In the expression below: v is the speed of an object, x is position, t is time, and a and b are constants. What are the dimensions of the constants? Please show how the blue box is correct. Thank you.

Answer 1

We know that for an physics expression to be correct, dimensions on both sides should be equal

v^2 = at^2v^2 + (bx)^2

dimension of v = meter/sec = L/T

dimension of t = sec = T

dimension of x = meter = L

So from these values:

dimension of v^2 = (meter/sec)^2 = m^2/sec^2 = L^2/T^2

Which means

dimension of at^2v^2 = dimension of (bx)^2 = L^2/T^2

at^2v^2 = L^2/T^2

dimension of a*dimension of t^2*dimension of v^2 = L^2/T^2

[a]*T^2*(L^2/T^2) = L^2/T^2

[a]*L^2 = L^2/T^2

[a] = (L^2/T^2)/L^2 = 1/T^2

Similarly

b^2*x^2 = L^2/T^2

[b]^2*L^2 = L^2/T^2

[b]^2 = 1/T^2

[b] = sqrt [1/T^2]

[b] = 1/T

Correct option is 7.

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