Question

P = A sin (Bt + Ct2) + x
Here t is time and x is length. The dimensions of AB/C
will be
[M°LT']
[MºLT-2
G22
[MLT-1
[MºL2T-1]​

Answer 1

The dimensions of AB/C is [M⁰LT]

Therefore, option (1) is correct.

Explanation:

Given:

Equation

$P=A\sin (Bt+Ct^2)+x$

Where t is time and x is length

To find out:

Dimensions of AB/C

Solution:

Since x is length therefore, P and $A\sin (Bt+Ct^2)$ will also have the dimensions of length

Also because the sine of something will be a dimensionless quantity

Therefore,

The dimensions of A will be that of the dimensions of length i.e. [L]

Also the quantity whose sine is been taken should be dimensionless

Therefore,

B will have dimensions of inverse of time i.e. [T⁻¹]

And C will have dimensions of inverse of square of time i.e. [T⁻²]

Thus,

Dimensions of AB/C

= [L][T⁻¹]/[T⁻²]

= [LT]

= [M⁰LT]

Hope this answer is helpful.

Know More:

Q: If x=a+bt+ct2 where x is in metres and t is in seconds.What is the unit of c?

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