Planck's constant has dimensions …………….

Explanation

To find the dimensions of Planck's constant, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship**: We start with the formula relating energy (E), Planck's constant (h), and frequency (f):
\[ E = h \cdot f \]

2. **Rearrange the formula**: To express Planck's constant in terms of energy and frequency, we rearrange the equation:
\[ h = \frac{E}{f} \]

3. **Identify the dimensions**: Next, we need to find the dimensions of energy (E) and frequency (f):
- The dimension of energy (E) is given by:
\[ [E] = M L^2 T^{-2} \]
- The dimension of frequency (f) is the reciprocal of time:
\[ [f] = T^{-1} \]

4. **Substitute the dimensions**: Now we can substitute these dimensions into our expression for Planck's constant:
\[ [h] = \frac{[E]}{[f]} = \frac{M L^2 T^{-2}}{T^{-1}} \]

5. **Simplify the expression**: When we divide by \(T^{-1}\), it is equivalent to multiplying by \(T^{1}\):
\[ [h] = M L^2 T^{-2} \cdot T^{1} = M L^2 T^{-1} \]

6. **Final result**: Therefore, the dimensions of Planck's constant (h) are:
\[ [h] = M L^2 T^{-1} \]

### Conclusion:
The dimensions of Planck's constant are \(M L^2 T^{-1}\).

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