Question

The spaceship Intergalactica lands on the surface of the uninhabited Pink Planet, which orbits a rather average star in the distant Garbanzo Galaxy. A scouting party sets out to explore. The party's leader–a physicist, naturally–immediately makes a determination of the acceleration due to gravity on the Pink Planet's surface by means of a simple pendulum of length 1.081.08 m. She sets the pendulum swinging, and her collaborators carefully count 101101 complete cycles of oscillation during 2.00×1022.00×102 s. What is the result? acceleration due to gravity:acceleration due to gravity: m/s2

Answer 1

Complete Question

The spaceship Intergalactica lands on the surface of the uninhabited Pink Planet, which orbits a rather average star in the distant Garbanzo Galaxy. A scouting party sets out to explore. The party's leader–a physicist, naturally–immediately makes a determination of the acceleration due to gravity on the Pink Planet's surface by means of a simple pendulum of length 1.08m. She sets the pendulum swinging, and her collaborators carefully count 101 complete cycles of oscillation during 2.00×102 s. What is the result? acceleration due to gravity:acceleration due to gravity: m/s2

Answer:

The acceleration due to gravity is  $g = 167.2 \ m/s^2$  

Explanation:

From the question we are told that

     The length of the simple pendulum is $L = 1.081.08 \ m$

      The number of cycles is  $N = 101$

       The time take is  $t = 2.00 *10^{2 \ }s$

Generally the period of this oscillation is mathematically evaluated as

         $T = \frac{N}{t }$

substituting values

         $T = \frac{101}{2.0*10^2 }$

        $T = 0.505 \ s$

The period of this oscillation is mathematically represented  as

               $T = 2 \pi \sqrt{\frac{l}{g} }$

making g the subject of the formula we have

              $g = \frac{L}{[\frac{T}{2 \pi } ]^2 }$

              $g = \frac{4 \pi ^2 L }{T^2 }$

Substituting values

               $g = \frac{4 * 3.142 ^2 * 1.08 }{505.505^2 }$

               $g = \frac{4 * 3.142 ^2 * 1.08 }{0.505^2 }$  

              $g = 167.2 \ m/s^2$