If energy (E), momentum (p) and force (F) are chosen as fundamental units. The dimensions of mass in new system is

If energy (E), momentum (p) and force (F) are chosen as fundamental un

1.	If energy (E), momentum (p) and force (F) are chosen as fundamental units. The dimensions of mass in new system is
Answer» `[E^(-1)p^(3)]` `[E^(-1)p^(2)]` `[E^(-2)p^(2)]` `[E^(-1)p]` Solution :The dimensions of E, p and F in terms of M, L and T are `[E]= [ML^(2)T^(-2)], [p]= [MLT^(-1)], [F]= [MLT^(-2)]` Let `m = kE^(a)p^(b)F^(c)` where k is a DIMENSIONLESS constant. `:.[M]= [ML^(2)T^(-2)]^(a)[MLT^(-1)]^(b)[MLT^(-2)]^(c)` or `[ML^(0)T^(0)]= [M^(a+b+c)L^(2A+b+c)T^(-2a-b-2c)]` EQUATING the powers of M, L and T we get a + b +c= 1, 2a + b + c = 0, -2a - b- 2c =0 Solving, we get a=-1, b= 2 and c=0 Hence `[m] = [E^(-1)p^(2)]`