Question

A student writes an expression for the momentum (p) of a body of mass (m) with total energy (E) and considering the duration of time (t) as p=√2mE/t. Check its correctness on dimensional analysis.

Answer 1

momentum is mass × velocity MLT^-1
RHS- ✓(M×ML^2T^-2/T)=MLT^-3/2 HENCE it is dimensionally incorrect

Answer 2

The dimensional formula of momentum is [M][L][T}^-1.

By dimensional analysis rt2mE/t comes out to be [M]^2[L]^2[T]^-3. Thus the formula found out has to be incorrect.