MHT CET · Physics · Thermal Properties of Matter

A clock pendulum having coefficient of linear expansion, $α = 9 \times 10^{- 7} / {}^{o}C$ has a period of $0.5 s$ at $20^{o} C .$ If the clock is used in a climate where the temperature is $30^{o} C,$ how much time does the clock lose in each oscillation? $(g = c o n s t a n t)$

A $2.5 \times 10^{- 7} s$
B $5 \times 10^{- 7} s$
C $1.125 \times 10^{- 6} s$
D $2.25 \times 10^{- 6} s$

Verified Solution

Answer & Solution

Correct Answer

(D) $2.25 \times 10^{- 6} s$

Step-by-step Solution

Detailed explanation

∵ \frac{d T}{T} = \frac{1}{2} ∙ (α \propto d T)

d T = (\frac{1}{2}) (\frac{1}{2}) (9 \times 10^{- 7}) (10)

d T = 2.25 \times 10^{- 6}

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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A clock pendulum having coefficient of linear expansion, α=9×10-7/Co has a period of 0.5s at 20oC. If the clock is used in a climate where the temperature is 30oC, how much time does the clock lose in each oscillation? g=constant

Step-by-step Solution

A clock pendulum having coefficient of linear expansion, $α = 9 \times 10^{- 7} / {}^{o}C$ has a period of $0.5 s$ at $20^{o} C .$ If the clock is used in a climate where the temperature is $30^{o} C,$ how much time does the clock lose in each oscillation? $(g = c o n s t a n t)$