Question

Find the dimensions of a,b and c in the following equation:
v=a sin[(bt+x)c]
where, v=velocity , t=time and x= distance​

Answer 1

Explanation:

as we know,

trignometric functions are dimentionless

so,

(bt+x)c=1----------(1)

btc+xc=1

btc=-xc

bt=-x

b=-x/t

so dimention of b is

$({LT}^{ - 1} )$

putting dimensions in equ. (1)

$({LT}^{ - 1} \times {T}^{ - 1} +L)c = 1$$( L + L)c = 1$

$(L + L)c = 1$

$L \times c = 1$

$c = L ^{ - 1}$

and the dimension of

a is equal to v

as the dimension of sin is 1

so,

$a = LT^{ - 1}$

$b = LT ^{ - 1}$

$c = L ^{ - 1}$