TS EAMCET · Physics · Motion In One Dimension

If $E$ and $E_{0}$ represent the energies, $t$ and $t_{0}$ represent the times, in which of the following is dimensionally correct relation?

A $E = E_{0} e^{- t}$
B $E = E_{0} t_{0} e^{- t / t_{0}}$
C $E = E_{0} t_{0} e^{- t^{2}}$
D $E = E_{0} e^{- t / t_{0}}$

Verified Solution

Answer & Solution

Correct Answer

(D) $E = E_{0} e^{- t / t_{0}}$

Step-by-step Solution

Detailed explanation

The dimensional formula for E=E0e-t/t0 as e-t/t0 is a dimensionless quantity. In the question, E and E0 represents the energies. E is the time-averaged energy of the oscillator which is dimensionally represented as ML2T-2 and E0 is the total energy of an undamped oscillator…

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 represent the energies, t and t0 represent the times, in which of the following is dimensionally correct relation?

Step-by-step Solution

If $E$ and $E_{0}$ represent the energies, $t$ and $t_{0}$ represent the times, in which of the following is dimensionally correct relation?