Chapter MPS, Problem 7.6MPS

(a)

To determine

To Draw: The graph of the given function.

Explanation of Solution

Given:

  $\begin{array}{l}l=\text{length of a pendulum}\\ g=9.8m/s^2\end{array}$

Formula Used:

  $f\left(l\right)=2\pi \sqrt{\left(\frac{l}{g}\right)}$

Calculation:

  $\begin{array}{llll}l\hfill & 0\hfill & 9.8\hfill & 39.2\hfill \\ f\left(l\right)\hfill & 0\hfill & 6.18\hfill & 12.36\hfill \end{array}$

  

Conclusion:

Thus the graph has been drawn.

(b)

To determine

To Find:Length of the pendulum for the given period of time.

Answer to Problem 7.6MPS

  $89cm$

Explanation of Solution

Given:

  $\begin{array}{l}l=\text{length of a pendulum}\\ g=9.8m/s^2\\ T=TimePeriod=1.9\sec \end{array}$

Formula Used:

  $f\left(l\right)=2\pi \sqrt{\left(\frac{l}{g}\right)}$

Calculation:

  $\begin{array}{l}l=\text{length of a pendulum}\\ g=9.8m/s\\ T=TimePeriod\\ f\left(l\right)=2\pi \sqrt{\left(\frac{l}{g}\right)}\\ T=f\left(l\right)=1.9\sec \\ \Rightarrow 1.9=2\pi \sqrt{\left(\frac{l}{g}\right)}\\ \Rightarrow {\left(\frac{1.9}{2\times \frac{22}{7}}\right)}^2=\frac{l}{9.8}\\ \Rightarrow l=\frac{17689}{193600}\times 9.8=0.89m\\ \Rightarrow l=89cm\end{array}$

Conclusion:

Thus the required length of the pendulum is $89cm$ .