TS EAMCET · Physics · Motion In One Dimension

Consider an expression $Q V = k P T L^{α}$ where $V, P, T, L$ are volume, pressure, time, and length respectively. The quantity $[Q]$ has dimension $M L^{- 1} T^{- 1} . k$ is a dimensionless constant. The value of the integer $α$ is:

A $2$
B $- 2$
C $3$
D $- 1$

Verified Solution

Answer & Solution

Correct Answer

(C) $3$

Step-by-step Solution

Detailed explanation

The expression given in the question is, QV=kPTLα, here the dimension of pressure, volume, time and length are, ML-1T-2, L3, T & L, it means, QV=kPTLα⇒ML-1 T-1L3=ML-1T-2×T×Lα⇒ML2 T-1=ML-1+α T-1 On…

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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Consider an expression QV=kPTLα where V, P, T, L are volume, pressure, time, and length respectively. The quantity Q has dimension ML-1 T-1. k is a dimensionless constant. The value of the integer α is:

Step-by-step Solution

Consider an expression $Q V = k P T L^{α}$ where $V, P, T, L$ are volume, pressure, time, and length respectively. The quantity $[Q]$ has dimension $M L^{- 1} T^{- 1} . k$ is a dimensionless constant. The value of the integer $α$ is: