Question

Page 2 of 2 3. Commander Warf has landed on a moon like object and is instructed to determine its gravitational strength. He constructs a simple pendulum of mass 1.75 kg and length 1008 mm and observes 30 full swings in 2 min and 28.00 s. What does he deduce the acceleration of gravity of this object to be?

Answer 1

Gravitational acceleration of the object = g

Mass attached to the simple pendulum = M = 1.75 kg

Length of the simple pendulum = L = 1008 mm = 1.008 m

The simple pendulum makes 30 full swings in 2min 28 sec (148 sec).

Time period of one oscillation = T = 148/30 sec = 4.933 sec

Time period of oscillation for a simple pendulum is given by,

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

Squaring both sides,

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

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

$g = \frac{4\pi ^{2}(1.008)}{(4.933)^{2}}$

g = 1.635 m/s²

Acceleration of gravity of this object = 1.635 m/s²