Question

Given that force F is given by, $F=P{t}^{-1}+Qt$, where t is the time. The unit of P is same as that of

• A. velocity
• B. acceleration
• C. displacement
• D. momentum

Answer 1

The correct option is D momentum

According to the principle of homogeneity of dimension, an equation is dimensionally correct when each term has same dimension on both sides of the equation.

Since left side has dimension of force so the term $P{t}^{-1}$ will have also dimension of force.

Thus, $\left[P\right]\left[T^{-1}\right]=\left[F\right]=\left[ML{T}^{-2}\right]$

or $\left[P\right]=\left[ML{T}^{-1}\right]$

We know that the dimension of momentum is $\left[p\right]=\left[ML{T}^{-1}\right]$