A plumb bob ( a mass m hanging on a string) is deflected from the vertical by an angle θ due to a massive mountain nearby (Fig. 6-30). ( a ) Find an approximate formula for 6 in terms of the mass of the mountain, m M , the distance to its center, D M , and the radius and mass of the Earth, ( b ) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m. Assume its mass per unit volume is 3000 kg per m 3 . ( c ) Estimate the angle θ of the plumb bob if it is 5 km from the center of Mt. Everest. FIGURE 6-30
A plumb bob ( a mass m hanging on a string) is deflected from the vertical by an angle θ due to a massive mountain nearby (Fig. 6-30). ( a ) Find an approximate formula for 6 in terms of the mass of the mountain, m M , the distance to its center, D M , and the radius and mass of the Earth, ( b ) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m. Assume its mass per unit volume is 3000 kg per m 3 . ( c ) Estimate the angle θ of the plumb bob if it is 5 km from the center of Mt. Everest. FIGURE 6-30
A plumb bob (
a
mass
m
hanging on a string) is deflected from the vertical by an angle θ due to a massive mountain nearby (Fig. 6-30). (a) Find an approximate formula for 6 in terms of the mass of the mountain, mM, the distance to its center, DM, and the radius and mass of the Earth, (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m. Assume its mass per unit volume is 3000 kg per m3. (c) Estimate the angle
θ
of the plumb bob if it is 5 km from the center of Mt. Everest.
Use the data of Table 7.3 to find the point between Earth and the Sun at which an object can be placed so that the net gravitational force exerted by Earth and the Sun on that object is zero.
A space rocket of mass 1500kg travelled from the Earth to the Moon, whose centres are separated by 3.8 x 108 m. Calculate the magnitude and direction of the resultant force of gravity due to the Earth and Moon, on the space rocket, when it is midway between their centres.
Consider a body of mass m moving in the gravitational field of nearly constant value of g Let it makes an angle 8 with the horizontal. Find the horizontal distance covered by it during time interval t. Also find the its Range.
Chapter 6 Solutions
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