Question

The position y of the oscillating particle is given by y= A sin (Bx +Ct+D) where A, B ,C and D are the constants . Then select the correct option
1) the dimension of AB is [L]
2) the dimension of C/D is [T^-1]
3) the dimension of DC/B is [L^2T-3]
4) A is dimensionless quantity

Answer 1

The dimension of C/D is [T¯¹]

Given : The position y of the oscillating particle is given by y = A sin (Bx +Ct+D) where A, B ,C and D are the constants .

To find : The position y of the oscillating particle is given by y = A sin (Bx +Ct+D).

dimension of y = dimension of A

so, dimension of A = [L]

we know sine function is a dimensionless quantity.

so, (Bx + Ct + D) is a dimensionless quantity.

⇒Bx , Ct and D are also dimensionless quantities .

now, dimension of B × dimension of x = 1

⇒dimension of B = 1/[L] = [L¯¹]

similarly, dimension of C = 1/dimension of t = 1/[T] = [T¯¹]

dimension of D = [M^0L^0T^0]

now you can find,

dimension of AB = [L][L¯¹] = [M^0L^0T^0]

dimension of C/D = [T¯¹]/1 = [T¯¹]

Therefore option (2) is correct choice.