Question

The dimensional formula for w in the relation y = A sin wt

Answer 1

Here A = Amplitude => [ A ] = [ L ]

and

Sine of any angle = Perpendicular / hypotenuse = Ratio of two sides of a Right angle triangle

=> sin ( wt ) is Dimensionless quantity i . e ,

Sin ( wt ) has no dimensions

therefore ,

Dimensional formula of y

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

Answer 2

Answer:

Dimensional formula of w = $[T^{-1}]$

Explanation:

In relation  y = A sin wt;  w represents the angular velocity; and t denotes time;

Dimensions of time = $[sec]=[T]$

Unit of angular velocity is  $rad/s$

Radian is the measure of the angle.

We know that angle is the ratio of length arc it subtends to the radius of the circle of which it is a part.

Therefore, the dimension of angle is $[M^0L^0T^0]$

Hence, dimensions of w = $\frac{[rad]}{[sec]}=\frac{[M^0L^0T^0]}{[T]} =[T^{-1}]$

#SPJ2