A plumb bob (a mass m hanging on a string) is deflected from the vertical by an

Question

A plumb bob (a mass m hanging on a string) is deflected from the vertical by an angle theta due to a massive mountain (Figure .1) Find the approximate formula for theta in terms of the mass of the mountain mM, the distance to its center DM, and the radius and mass of the earth. Express your answer in terms of the variables mM, DM, RE, mE, and appropriate constants Make a rough estimate of the mass of Mt. Everest assuming it has the shape of cone 4000m high and base of diameter 4000m. Assume its mass pet unit volume K 3000 kg per m^3 Express your answer to one significant figure and include the appropriate units

Explanation / Answer

Tsin@ = Fm

and Fm = GMm *m / Dm^2

Tsin@ = GMm * m/ Dm^2 .....(i)

Tcos@ = mg

g = GMe / Re^2

Tcos@ = Gme*m / Re^2 ......(ii)

(i) / (ii)

tan@ = Mm Re^2 / Me Dm^2

@ = tan^-1 [ Mm Re^2 / Me Dm^2 ]

B) density = 3000 kg/m^3

Volume of a cone = pi r^2 h / 3

V = pi x 2000^2 x 4000 / 3

V = 1.68 x 10^10 m^3

mass = volume x density

= 5.03 x 10^13 kg

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