Chapter 12.7, Problem 7P

To determine

To calculate: The time 150 cm pendulum will take to swing, if it takes a 100 cm pendulum 1 sec to swing from one side to other also given the length of a pendulum varies directly as the square of the time in seconds to swing from one side to other.

Answer to Problem 7P

The time pendulum takes to swing is $t=1.22$ .

Explanation of Solution

Given information:

The length of a pendulum varies directly as the square of the time in seconds to swing from one side to other

Let, Length of pendulum is l.

Time taken by it to swing one side to other t.

So, $l\prec t^2$

Let k be a constant

  $l=k\cdot t^2$

Put the value of l and t in equation 1 to get k

  $100=k\cdot {\left(1\right)}^2$

  $k=100$

Put the value of k and d in equation 1 to get l..

  $l=k\cdot t^2$

  $150=100\cdot t^2$

  $t^2=\frac{150}{100}$

  $t=\sqrt{1.5}$

  $t=1.22$