Question

The period of oscillation of pendulum clock change from day to night. Brass is used in the pendulum. Temperature changes from 35ºC to 20ºC from day to night. In 12 hours the time that can be gained or lost is- (Coefficient of linear expansion for brass = 2 × 10^–5/ºC)

Answer 1

In 12 hours the clock will lose 8.64 seconds

Explanation :

We know that the linear expansion of material can be given by

L' = L(1 + αt)

where α = coefficient of linear expansion = 2 x 10⁻⁵

t = change in temperature = 20-35 = -15°C

hence ,

L' = L(1 + 2 x 10⁻⁵ x -15)

=> L' = 0.9997L

we know that time period of a pendulum is given by

T = 2π√L/g

for the decreased length time period is given by,

T' = 2π√L'/g

Hence,

T'/T = √(L'/L) = √0.9997 = 0.9998

Hence for T = 1 sec

T' = 0.9998 sec

hence time lost in 1 sec = 1 - 0.9998 = 0.0002 sec

For 12 hours time lost = 12 x 3600 x 0.0002 = 8.64 sec

Hence in 12 hours the clock will lose 8.64 seconds