Question

The mathematical relationship between three physical properties is given by a=b^2/c. If the dimension of b is [L]/[T], and the dimension of c is [L]. Which of the following is the dimension of a?

A) [L]
B) [L]/[T]^2
C) [L]/[T]
D) [T]
E) [L]^2/[T]^2

Answer 1

The dimension of physical property a is [L]/[T]^2, meaning that the correct answer is option B.

Step-by-step explanation:

The student's question asks us to find the dimension of physical property a when a = b2/c, and we are given the dimensions of physical properties b and c. The dimension of b is [L]/[T], which means it has dimensions of length over time. The dimension of c is [L], which is simply the dimension of length

To find the dimension of a, we will use the rule that multiplying a quantity by itself squares its dimension, and dividing by another quantity reduces the dimension accordingly. Thus, the dimension of b2 would be ([L]/[T])2 which equals [L2]/[T2]. When we divide that by the dimension of c, [L], we get [L2]/[T2 divided by [L] which simplifies to [L]/[T2]. Therefore, the correct dimension of a is [L]/[T2], which corresponds to option B.