Question

If the displacement y of a particle is
y = A sin (pt + cx), then
1) the dimensions of p are M°LºT
2) the dimensions of q are M°LT°
3) the dimensions of p/q are M°LT-
4) the dimensions of pq are M°LT-1

Answer 1

Given : If the displacement y of a particle is y = A sin(pt + qx).

To check : 1) the dimensions of p are M°LºT

2) the dimensions of q are M°LT°

3) the dimensions of p/q are M°LT-1

4) the dimensions of pq are M°LT-1

solution : y = A sin(pt + cx)

we know, trigonometric functions are dimensionless quantities.

so, (pt + qx) is a dimensionless quantity.

so, pt and qx are dimensionless quantities.

now, dimensions of p × dimensions of t = 1

⇒dimensions of p = 1/dimensions of t = [M^0L^0T^-1]

similarly, dimensions of c × dimensions of x = 1

⇒dimensions of q = 1/dimensions of x

= [M^0L^-1T^0]

then dimensions of p/q = [M^0LT^-1]

Therefore it is clear that option (3) is correct choice.