The dimensional formula of product and quotient of two physical quantities A and B are given by `[AB]=[ML^(2)T^(-2)], [A/B]=[MT^(-2)]`. The quantities A and B respectively are

Options

A. force and velocity
B. force and displacement
C. Momentum and dispalcement
D. Work and velocity

Explanation

To solve the problem, we need to find the physical quantities A and B given their dimensional formulas for the product and quotient.

### Step-by-step Solution:

1. **Write down the given dimensional formulas:**
- For the product \( AB \):
\[ [AB] = [ML^2T^{-2}] \]
- For the quotient \( \frac{A}{B} \):
\[ \left[\frac{A}{B}\right] = [MT^{-2}] \]

2. **Assign the dimensions of A and B:**
- Let the dimension of \( A \) be \( [A] = [M^a L^b T^c] \)
- Let the dimension of \( B \) be \( [B] = [M^d L^e T^f] \)

3. **Express the dimensions for the product \( AB \):**
\[ [AB] = [A][B] = [M^a L^b T^c][M^d L^e T^f] = [M^{a+d} L^{b+e} T^{c+f}] \]
From the given \( [AB] = [ML^2T^{-2}] \), we can equate the exponents:
- \( a + d = 1 \) (1)
- \( b + e = 2 \) (2)
- \( c + f = -2 \) (3)

4. **Express the dimensions for the quotient \( \frac{A}{B} \):**
\[ \left[\frac{A}{B}\right] = \frac{[A]}{[B]} = \frac{[M^a L^b T^c]}{[M^d L^e T^f]} = [M^{a-d} L^{b-e} T^{c-f}] \]
From the given \( \left[\frac{A}{B}\right] = [MT^{-2}] \), we can equate the exponents:
- \( a - d = 1 \) (4)
- \( b - e = 0 \) (5)
- \( c - f = -2 \) (6)

5. **Solve the equations:**
- From (1) and (4):
\[ a + d = 1 \quad \text{and} \quad a - d = 1 \]
Adding these two equations:
\[ 2a = 2 \implies a = 1 \]
Substituting \( a = 1 \) into (1):
\[ 1 + d = 1 \implies d = 0 \]

- From (2) and (5):
\[ b + e = 2 \quad \text{and} \quad b - e = 0 \]
Adding these two equations:
\[ 2b = 2 \implies b = 1 \]
Substituting \( b = 1 \) into (2):
\[ 1 + e = 2 \implies e = 1 \]

- From (3) and (6):
\[ c + f = -2 \quad \text{and} \quad c - f = -2 \]
Adding these two equations:
\[ 2c = -4 \implies c = -2 \]
Substituting \( c = -2 \) into (3):
\[ -2 + f = -2 \implies f = 0 \]

6. **Summary of dimensions:**
- \( A \): \( [A] = [M^1 L^1 T^{-2}] \) which represents force (since \( F = ma \)).
- \( B \): \( [B] = [M^0 L^1 T^0] \) which represents displacement.

### Final Answer:
- The physical quantities A and B are:
- \( A \) is Force
- \( B \) is Displacement