Which of the following has the same dimensions?

Options

A. Impulse and momentum
B. Specific heat and latent heat
C. Moment of inerita and force
D. Thrust and surface tension

Explanation

To solve the question of which of the following has the same dimensions, we need to analyze each option provided.

### Step-by-Step Solution:

1. **Understanding Impulse and Momentum (Option A)**:
- Impulse is defined as the change in momentum.
- Momentum (p) is given by the formula:
\[ p = mv \]
where \( m \) is mass and \( v \) is velocity.
- The dimensions of momentum are:
\[ [p] = [M][L][T^{-1}] \]
- Since impulse is equal to change in momentum, it also has the same dimensions:
\[ [\text{Impulse}] = [M][L][T^{-1}] \]
- Therefore, Option A has the same dimensions.

2. **Analyzing Specific Heat and Latent Heat (Option B)**:
- Specific heat is defined as the amount of heat required to change the temperature of a unit mass by one degree Celsius. Its dimensions are:
\[ [\text{Specific Heat}] = [M^{0}][L^{2}][T^{-2}][\Theta^{-1}] \]
- Latent heat is the heat required to change the state of a substance without changing its temperature. Its dimensions are:
\[ [\text{Latent Heat}] = [M^{0}][L^{2}][T^{-2}][\Theta^{-1}] \]
- While both have similar dimensions, they are not the same conceptually as specific heat depends on temperature changes while latent heat does not.

3. **Analyzing Moment of Inertia and Force (Option C)**:
- Moment of inertia (I) is given by:
\[ I = m r^2 \]
where \( r \) is the radius. Its dimensions are:
\[ [I] = [M][L^{2}] \]
- Force (F) is defined as:
\[ F = ma \]
where \( a \) is acceleration. Its dimensions are:
\[ [F] = [M][L][T^{-2}] \]
- Since the dimensions of moment of inertia and force are different, Option C is incorrect.

4. **Analyzing Thrust and Surface Tension (Option D)**:
- Thrust is a force, so its dimensions are:
\[ [\text{Thrust}] = [M][L][T^{-2}] \]
- Surface tension is defined as force per unit length. Its dimensions are:
\[ [\text{Surface Tension}] = \frac{[\text{Force}]}{[\text{Length}]} = \frac{[M][L][T^{-2}]}{[L]} = [M][T^{-2}] \]
- Since the dimensions of thrust and surface tension are different, Option D is also incorrect.

### Conclusion:
The only option that has the same dimensions is **Option A: Impulse and Momentum**.