Which of the following cannot be the group of fundamental quantities.
(Here M is mass, L is length, T is time, F is force, A is acceleration, V is velocity)

Options

A. (M,L,V)
B. (F,L,T)
C. (M,L,T)
D. (A,V,L)

Answer

To determine which of the given groups cannot be a collection of fundamental quantities, we first need to understand what fundamental quantities are. Fundamental quantities are the basic physical quantities that cannot be derived from other quantities. In the context of physics, the fundamental quantities include:

- Mass (M)
- Length (L)
- Time (T)

Now, let's analyze each of the provided options:

1. **Option A: Mass (M), Length (L), Velocity (V)**
- Here, we have:
- Mass (M) = M
- Length (L) = L
- Velocity (V) = L/T (which can be expressed in terms of fundamental quantities)
- This group contains fundamental quantities (M, L) and a derived quantity (V), but it is still valid since M and L are fundamental.

2. **Option B: Mass (M), Length (L), Time (T)**
- Here, we have:
- Mass (M) = M
- Length (L) = L
- Time (T) = T
- All three are fundamental quantities. This group is valid.

3. **Option C: Force (F), Length (L), Time (T)**
- Here, we have:
- Force (F) = MLT^(-2) (derived from fundamental quantities)
- Length (L) = L
- Time (T) = T
- This group contains one derived quantity (F) and two fundamental quantities (L, T). This group is also valid.

4. **Option D: Acceleration (A), Velocity (V), Length (L)**
- Here, we have:
- Acceleration (A) = LT^(-2) (derived from fundamental quantities)
- Velocity (V) = LT^(-1) (derived from fundamental quantities)
- Length (L) = L
- This group contains no fundamental quantities (M is absent). Both A and V are derived quantities, making this group invalid as a collection of fundamental quantities.

Based on the analysis, the group that cannot be a collection of fundamental quantities is:

**Answer: Option D (Acceleration, Velocity, Length)**