00:01
Question is saying that you have just gotten a pendulum clock as a gift.
00:05
The pendulum consists of a disc whose center is formally attached to the center of solid rod.
00:11
Both the disc and the rod are made of solid brass.
00:16
Being a science major, you are interested in precision and wonder whether the differences in the rate at which the clock run between the summer and winter will be noticeable.
00:26
So you do a calculation to find out.
00:29
Fine.
00:30
The average temperature in your house is around 10 degree fahrenheit's warmer in the summer compared to the winter and looking in your physics textbook.
00:40
You find the coefficient of linear expansion of brass.
00:45
So alpha value they have given that is coefficient of linear expansion is 19 into 10 to the power minus 6 degrees celsius.
00:58
Correct per degree celsius fine now for a pendulum for a pendulum time period is given by you know it 2 pi square root of l upon g where l is the length of the string j is gravitational acceleration acceleration due to gravity fine now find the change in time period and the ratio of with the correct time period so it will be nothing but one by two delta l upon l this is the equation for a change in time period with respect to time period itself from here if we calculate delta l that is change in length from the equation of linear expansion delta t is at a temperature change so temperature change in winter and summer they have given 10 degrees celsius so delta t will be 10 degrees celsius now we put the values 19 into 10 to the power minus x okay into 10 upon 1 .8 because it is given in fahrenheit 10 degree fahrenheits they have given you to convert into celsius so we'll do it 1 by 1 .8 so from here we get the value of delta l upon l as 1 .056 into 10 to the power minus 4 if we put the value of this delta l here in this particular equation, we'll get delta t upon t.
02:47
It will be 5 .28 into 10 to the bar minus 5...