Question

The volume of an object is given as a function of time by V = A + B t + C t4 . Find the dimension of the constant C

Answer 1

The dimension of the constant C in the volume function V = A + Bt + Ct4 is [L3]/[T4], which ensures each term in the equation has the same dimension as volume.

Step-by-step explanation:

To find the dimension of the constant C in the given volume function of an object, V = A + Bt + Ct4,

Since A and Bt must have the dimensions of volume, B has dimensions of volume/time ([L3]/[T]). To satisfy this, C must have dimensions of volume divided by time to the fourth power, which is [L3]/[T4]. This ensures that when multiplied by t4, the units of time cancel out appropriately, giving a term with a volume dimension, consistent with the other terms in the equation.

Thus, the dimension of the constant C is [L3]/[T4]

Answer 2

The dimensions of constant C are of
`[L^(3)T]^(-4)`

Step-by-step explanation:

It is given that

`V(t)=A+Bt+Ct^(3)`

Since the dimensions of volume are
`[L^(3)]`

Each of the term shall have a dimension of
`[L^(3)]` since they are in addition.

Thus for third term we can write

Thus we have

`[L^(3)]=[C][T^(4)]\\\\\therefore [C]=[L^(3)][T^(-4)]`