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Question

# A pendulum clock gives correct time at 20o (at a place where g=10m/s2) The pendulum consists of a light steel rod connected to a heavy ball. If it is taken to a different place (whereg=10)01m/s2 at what temperature the pendulum gives correct time (αofsteelis10−5/oC) [2007 E ]

A
30oC
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B
60oC
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C
1000oC
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D
120oC
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Solution

## The correct option is D 120oCWe know that,For a pendulum clockT=2n√lg⇒T=2π(l)1/2(g)−1/2So, ΔTT=Δl2l−Δg2gHere, ΔT=0 and Δl=l∝ΔT(Thermal expansion)So,OT=Δl2l−Δg2g⇒Δgg=Δll⇒Δgg=αeΔTe⇒10.01−1010=(10−5)(T−20)⇒10−310−5=T−20⇒T=102+20=120oCOption D is correct.

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