Question

Find the dimensions of a,b and c .....
y = 4 Sin at + 3 Cos bt - ct where y stands for
distance and t stands for time.
​

Answer 1

y=m

t=s

sin() and cos() are dimensionless

therefore

at=dimensionless

this is only possible when a=t⁻¹

similarly

b=t⁻¹

dimensions of y and ct must be same only then we can equate them

y=m

ct=m

this is only possible when c=mt⁻¹

therefore

a=b=[M⁰L⁰T⁻¹]

c=[M⁰L¹T⁻¹]