UPSEE Solved Model Paper 1

Let dimension of Energy [E] = [G]a [V]b [T]c
Dimension of ‘E’ when fundamental unit M(mass), L (length) and T(time) is given by
[ML2T–2]
So, [ML2T–2] = [G]a[V]b[T]c
On putting dimension of G and V in term of fundamental unit M, L and T
[ML2T–2] = [M–1L3T–2]a[LT–1]b[T]c
[ML2T–2] = [M]−a[L]3a+b[T]–2a−b+c
Compare the power of [M], [L] and [T]
–a =1 …(i)
3a + b = 2 …(ii)
–2a -b + c = – 2 …(iii)
a = -1, b = 5, c = 1
So, dimension of Energy
= [G]–1[V]5[T]1
= [G–1V5T]