Suppose the volume V of some object hap-
pens to depend on time t according to the
equation V (t) = At3+B/t
, where A and B are
constants. Let L and T denote dimensions of
length and time, respectively.
What is the dimension of the constant A?
1. L2/T
2. L/T3
3. L3/T3
4. L/T
5. L3
ยท T3
the 3 is actually a cubed as is the 2
There is no L in your Eq.
To determine the dimension of the constant A in the equation V(t) = At^3 + B/t, we need to analyze the dimensions of each term.
In the equation, V(t) represents volume, which has the dimension of length cubed (L^3), as volume is typically measured in cubic units.
The first term, At^3, represents the contribution of A to the volume function. The dimension of t^3 is (T^3), where T represents time.
To match the dimension of L^3 for the volume, the dimension of A must be L^3/T^3.
Therefore, the correct answer is 3. L^3/T^3.