Question

46. A physical quantity f depends on the dimensionful quantities x and y as follows:
f = AX + B exp(cy).
Which of the following do not have the same dimensions:
A. f and B
B. c and y-!
C. x and B/A
D. X and A
47. The period of oscillation of a simple pendulum of length L suspended from the roof of a rocke
accelerating upwards wil a constant acceleration (g) is given by:
A. 00
B. 0
C. 21
L
V 2g
D. 27​

Answer 1

Answer:

46 . In this question the since c and y are inside the exponential their multiplication must be dimensionless. And since exponential part is dimension less so f and B have same dimension.

c and y-1 have same dimension because cy is dimensionless.

Since the dimension of Ax must be same as B, B=A is not possible.

x and A may not have same dimension. Depending on the dimension of quantity f, A may be dimensionless or can have any other dimension.

So D. is the correct answer.

Answer 2

f = AX + B.$e^{cy}$

$e^{cy}$ has no dimension

so f , B have sane dimension

f=Ax ie x has dimension of l and

A has dimension of $\frac{f}{L}$ or $\frac{B}{L}$

ey is constant ie c and y-! have same dimension.