A plumb bob is deflected from the vertical by an angle theta due to a massive mo

Question

A plumb bob is deflected from the vertical by an angle theta due to a massive mountain nearby as seen in figure below.

A)    Make an estimate of the mass of Mt. Everest, assuming it has the shape of a cone 3800m high above its base, where the diameter of the base is equal to the distance from the perimeter of the base to the apex. In simpler terms, assume the base is a circle and the apex of the cone (the summit of Everest) is directly above the center of the base the height h. Any slice through this cone that includes the apex and any diameter of the base is an equilateral triangle, with all sides of the triangle equal to the diameter of the base. The density of rock is 3000 kg per cubic meter.

B)  Estimate the angle theta of the pendulum bob if it is 4.80km from the center of Mt. Everest.

Explanation / Answer

a) You have to assume distance to the centre of mass (well you don't have to, but otherwise there isn't really a good way to solve this problem... you'd need the shape of the mountain.) In this case, its just a simple matter of adding up the forces on the plumb bob.

Draw a right angle triangle. The force down is the force of gravity (mg) from the earth, the 'deflection' force is the force from the mountain (gmM/r^2).

The angle is then determined by trig.

(b) its a rough estimate. Work out the volume (a cone has 1/3 of the volume of a cylinder), estimate the density (a rock sinks in water...beyond that, you'd want to google for the density of a rock, or do some experiments).

c) is an application of the formula you worked out in (a)

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