Question

The mathematical relationship between three physical quantities is given by "a equals b squared times c." If the dimension of b is [M] and the dimension of c is [L], which one of the following choices is the dimension of a?

a. [ML]
b. [M²L]
c. [M²L²]
d. [ML²]

Answer 1

The dimension of the physical quantity a, represented as a equals b squared times c and with dimensions [M] for b and [L] for c, is [M²L].OPTION B.

Step-by-step explanation:

The question asks for the dimension of a physical quantity a where a equals b squared times c. Given the dimensions of b as [M] (mass) and c as [L] (length), we can calculate the dimension of a. Since b is squared, its dimension becomes [M]2, and when multiplied by c, which has a dimension of [L], we get the dimension of a to be [M]2L (mass squared times length).

Therefore, the correct answer to the question is b. [M2L], indicating that a has the dimension of mass squared times length.

The equation given is a = b²c. The dimension of b is M and the dimension of c is L. To find the dimension of a, we substitute the dimensions of b and c into the equation. Therefore, the dimension of a is [M²L].