Question

If the period of a pendulum is 2.0 seconds and the acceleration due to gravity is 9.8 meters/second2, what is the length of the cord on the pendulum?

Answer 1

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Answer 2

Answer:

The period of a pendulum is 2.0 seconds and the acceleration due to gravity is $g = 9.8\ m/s^2$the length of the cord on the pendulum is $0.9939m$

Explanation:

• The time period (T) of a simple pendulum is defined by the equation,

        $T = 2\pi \sqrt{\frac{l}{g} }$       ...(1)

       Where,

        g: the acceleration due to gravity.

        Squaring and rearranging equation (1),

        $T^2 = 4\pi ^2(\frac{l}{g} )$

         $l=\frac{g \mathrm{~T}^{2}}{4 \pi^{2}}$          ...(2)

         

• In the question, it is given that,

         $T = 2 s$      $g = 9.8\ m/s^2$

         We know,

         $\pi = 3.14$

        Then substitute these values into equation(2),

         $l=\frac{9.8\times \mathrm{~2}^{2}}{4 \times\ 3.14^{2}}$

            $= 0.9939 m$

         So we get,

• The length of the simple pendulum, $l =0.9939 m$