Guest

A pendulum clock gives correct time at 20 degree Celsius at a place where g= 9.800 m/s^2. The pendulum consists of a light steel rod connected to a heavy ball. It is taken to a different place where g=9.788 m/s^2. At what temperature will it give correct time?coefficient of linear expansion of steel = 12x 10^-6/ degree celsius.

A pendulum clock gives correct time at 20 degree Celsius at a place where g= 9.800 m/s^2. The pendulum consists of a light steel rod connected to a heavy ball. It is taken to a different place where g=9.788 m/s^2. At what temperature will it give correct time?coefficient of linear expansion of steel = 12x 10^-6/ degree celsius.

Grade:

1 Answers

SAGAR SINGH - IIT DELHI
878 Points
13 years ago

Dear student,

1st time

t = 2π√l/g
t = 2π√l/9.8 ------------->(1)

2nd time



t = 2π√L/G

L=l * (1 + 12x10^-6 * θ)

t = 2π√L/G
t = 2π√l*(1 + 12x10^-6 * θ)/9.788 ---------------->(2)

If it gives correct time, both "t"s of two occasions should be same
(1) = (2)

2π√l*(1 + 12x10^-6 * θ)/9.788 = 2π√l/9.8

l*(1 + 12x10^-6 * θ)/9.788 = l/9.8

1 + 12x10^-6 * θ / 9.788 = 1 / 9.8

1 + 12x10^-6 * θ = 9.788 / 9.8

1 + 12x10^-6 * θ = 0.9988

12x10^-6 * θ = -12*10^-4

10^-2 * θ = -1

θ = -100°C ( temperature difference )

Temperature - 20 = -100
Temperature = -80°C

 

Please feel free to ask your queries here. We are all IITians and here to help you in your IIT JEE preparation.

All the best.

Win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian.

Now you score 5+15 POINTS by uploading your Pic and Downloading the Askiitians Toolbar  respectively : Click here to download the toolbar..

 

Askiitians Expert

Sagar Singh

B.Tech, IIT Delhi

Think You Can Provide A Better Answer ?

ASK QUESTION

Get your questions answered by the expert for free