Concept explainers
(a)
The period of motion of pendulum for each lengths.
(a)
Answer to Problem 44P
The period of motion for length
Explanation of Solution
Write the expression for the time period of oscillation of a simple pendulum.
Here,
Conclusion:
Consider simple pendulum of length
Substitute
Consider simple pendulum of length
Substitute
Consider simple pendulum of length
Substitute
Tabulated form of the length of pendulum and the corresponding time periods is shown in Table 1 below.
Therefore, the period of motion for length
(b)
The average value of
(b)
Answer to Problem 44P
The average value of
Explanation of Solution
Write the expression for the time period of the simple pendulum.
Here,
Square expression (II) and rearrange to find
Write the expression to find the average acceleration due to gravity.
Here,
Write the expression to find the degree of closeness of the average value to the accepted value of acceleration due to gravity.
Here,
Conclusion:
Consider simple pendulum of length
Substitute
Consider simple pendulum of length
Substitute
Consider simple pendulum of length
Substitute
The tabulate form of values of time period, length and acceleration due to gravity is given in Table 2 below.
Substitute
Substitute
Therefore, the average value of
(c)
Plot
(c)
Answer to Problem 44P
Figure 1 gives the plot between
Explanation of Solution
From Table 2 obtain the values for length of pendulums and the corresponding time period of oscillations. Find the value of
Plot
Write the expression for
From equation (VI), slope of the graph is
Here,
Rearrange expression (VII) to find
Conclusion:
The slope of graph is got as
Therefore, Figure 1 gives the plot between
(d)
The level of closeness of
(d)
Answer to Problem 44P
The value of
Explanation of Solution
Write the expression to find the level of closeness of acceleration due to gravity from graph and accepted value of
Here,
Conclusion:
Substitute
Therefore, the value of
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Chapter 15 Solutions
Physics for Scientists and Engineers with Modern Physics, Technology Update
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