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Question Number 17117 by tawa tawa last updated on 01/Jul/17

A clock has a pendulum made of iron rod of length 2 . 5 m,

if the clock keeps accurate time at 0 ° C . By how much time will it be late

running at a temperature 30 ° C for 1 day . coefficient of linear expansivity of

iron is 1.2 \times 10^{- 5} per k .

Answered by ajfour last updated on 01/Jul/17

t = 2 π \sqrt{\frac{L}{g}}

t + △ t = 2 π \sqrt{\frac{L (1 + α △ T)}{g}}

= 2 π \sqrt{\frac{L}{g}} \times (1 + \frac{α △ T}{2})

t + △ t = t (1 + \frac{α △ T}{2})

\Rightarrow △ t = t (\frac{α △ T}{2})

or \frac{△ t}{t} = \frac{α △ T}{2}

time lost = \frac{△ t}{t} \times 86400 s

= \frac{α △ T}{2} \times 86400 s

= \frac{1.2 \times 10^{- 5} \times 30}{2} \times 86400 s

= \frac{1.2 \times 30 \times 0.864}{2} = 18 \times 0.864 s

= 15.552 s .

Commented by tawa tawa last updated on 01/Jul/17

God bless you sir . i really appreciate .