Question

33. A pendulum clock (made of metal) gives correct
time at 30°C. If the room temperature rises to
40°C then error in the clock per 10 hours would be
(a = 10-3/°C)
(1) 40 s
(2) 120 s
(3) 180 s
(4) 240 s
​

Answer 1

answer : option (3) 180 sec

given, initial temperature = 30°C

final temperature = 40°C

coefficient of linear expansion, α = 10^-3/°C

we know time period of a simple pendulum is given by, T = 2π√{l/g}

so, derivation of relation between temperature and length change is given as, ∆T/T = 1/2(α∆θ)

⇒∆T/10hours = 1/2 × 10^-3 × (40°C - 30°C)

= 1/2 × 10^-1

= 0.05 hour

= 0.05 × 3600 sec

= 180 sec

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Answer 2

$\huge\bold\purple{Answer:-}$

(3) 180 s