TS EAMCET · Physics · Units and Dimensions

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) $E = \frac{2 E_{0} L}{L_{0}}$ (B) $E = E_{0} e^{- \frac{2 L}{L_{0}}}$ (C) $E = 2 L e^{\frac{- L}{E_{0}}}$ (D) $E = 2 (\frac{E_{0}}{L_{0}}) \times e^{\frac{- L}{L_{0}}}$

A A,B only
B A,C only
C A,C,D only
D C,D only

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Answer & Solution

Correct Answer

(D) C,D only

Step-by-step Solution

Detailed explanation

Dimensions of energy =E=E0=ML2T-2 Dimensions of length =L=L0=M0L1T0 For A: LHS =ML2T-2 RHS =ML2T-2LL=ML2T-2 In this case, LHS=RHS For B: Exponent should be dimensionless. As we can see -2LL0=LL=M0L0T0 and LHS =ML2T-2 and RHS =ML2T-2 So in this case, LHS=RHS For C: Exponent…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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If E and E0 denote energies at time t and t0 respectively, and L and L0 distance from some point at t and t0 respectively, then which of the following equations can be declared to be incorrect on dimensional grounds (A) E=2E0LL0 (B) E=E0e-2LL0 (C) E=2Le-LE0 (D) E=2E0L0×e-LL0

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