If E and E 0 denote energies at time t and t 0 respectively, and L and L 0 distance from some point at t and t 0 respectively, then which of the following equations can be declared to be incorrect on dimensional grounds (A) E = 2 E 0 L L 0 (B) E = E 0 e - 2 L L 0 (C) E = 2 L e - L E 0 (D) E = 2 E 0 L 0 × e - L L 0

Step-by-step solution

Dimensions of energy = E = E 0 = M L 2 T - 2 Dimensions of length = L = L 0 = M 0 L 1 T 0 For A: LHS = M L 2 T - 2 RHS = M L 2 T - 2 L L = M L 2 T - 2 In this case, LHS=RHS For B: Exponent should be dimensionless. As we can see - 2 L L 0 = L L = M 0 L 0 T 0 and LHS = M L 2 T - 2 and RHS = M L 2 T - 2 So in this case, LHS=RHS For C: Exponent should be dimensionless but here - L 0 E 0 = M 0 L 1 T 0 M L 2 T - 2 = M - 1 L - 1 T 2 is not dimensionless therefore it is wrong. For D: Exponent should be dimensionless. Here