**Which of the following equations are dimensionally consistent?**

**Answer:**

**(A)** Consider the equation v = at

Carry out a dimension analysis on both sides.

The dimension of the left-hand side =

The dimensions on both sides are the same.

Thus, the equation v = at is **dimensionally consistent.**

**(B)** Consider the equation

Write the dimensions on both sides.

The dimension of the left-hand side =

The dimensions on both sides are different.

Thus, the equation is **dimensionally inconsistent.**

**( C)** Consider the equation

Carry out a dimension analysis on both sides.

The dimension of the left-hand side = **[ T ]**

The dimensions on both sides are different.

Thus, the equation is **dimensionally inconsistent.**

**(D)** Consider the equation

Carry out a dimension analysis on both sides.

The dimension of the left-hand side =

=

The dimension of the right-hand side

The dimensions on both sides are the same.

Thus, the equation is **dimensionally consistent.**