An astronaut arrives at a new planet, and gets out his simple device to determin

Question

An astronaut arrives at a new planet, and gets out his simple device to determine the gravitational acceleration there. Prior to this arrival, he noted that the radius of the planet was 7040 km. If his 0.400-m-long pendulum has a period of 1.0 s, what is the mass of the planet? Q2: A 6.0 kg planar figure is suspended at a point 10 cm from its center of mass. When it is oscillating with small amplitude, the period of oscillation is 2.7 s. Find the moment of inertia I about an axis perpendicular to the plane of the figure through the pivot point.

Explanation / Answer

Q2.

For rotational periodic motion

T = 2*pi*sqrt (I/mgD)

I = m*g*D*T^2/(4*pi^2)

given data

m = 6 kg

g = 9.81 m/sec^2

D = 10cm = 0.1

T = 2.7 sec

So,

I = 6*9.81*0.1*2.7^2/(4*pi^2)

I = 1.086 kg-m^2

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