# Gravitation: 4 Problems

1) The following formula represents the period of a pendulum,T.

T = 2π(l/g)

(a) What would be the period of a 1.8 m long pendulum on the moon's surface? The moon's mass is 7.34 1022 kg, and its radius is 1.74x10^6 m.

2) A force of 40.9 N is required to pull a 10.2 kg wooden block at a constant velocity across a smooth glass surface on Earth. What force would be required to pull the same wooden block across the same glass surface on the planet Jupiter?

3) A 1.1 kg mass weighs 10.78 N on Earth's surface, and the radius of Earth is roughly 6.4 106 m. (Use G = 6.67 10-11 N·m2/kg2.)

(a) Calculate the mass of Earth.

kg

(b) Calculate the average density of Earth.

kg/m3

4) An apparatus like the one Cavendish used to find G has a large lead ball that is 6.2 kg in mass and a small one that is 0.040 kg. Their centers are separated by 0.055 m. Find the force of attraction between them. (Use G = 6.67 10-11 N·m2/kg2.)

N

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1) The following formula represents the period of a pendulum.

T = 2π(l/g)

(a) What would be the period of a 1.8 m long pendulum on the moon's surface? The moon's mass is 7.34 1022 kg, and its radius is 1.74x10^6 m.

The time period T of a simple pendulum of length l is given by

Here g is the acceleration due to gravity at the place of experiment.

Now the acceleration due to gravity at the surface of a planet is given by

Here G is universal gravitation constant, M is the mass of the planet and R is the radius of the planet.

Thus the acceleration due to gravity near the surface of moon will be given by the same formula.

Here mass of the moon M = 7.34*1022 kg

Radius of moon R = 1.74*106 m

And gravitation constant G = 6.67*10-11 N m2/kg2

Thus the acceleration at the surface of moon will be

m/s2

Thus the time period of the pendulum of length l = 1.80 m on the surface of moon is given by

Thus the period of small oscillation of pendulum will be 6.6 s.

2) A force of 40.9 N is ...

#### Solution Summary

4 problems related to gravitation and gravity are solved and explained in the solution.

Physics Questions

1. (a) Calculate the mass of the earth given the acceleration of gravity at the north pole is 9.830 m/s^2 and the radius of the earth is 6371 km from pole to pole. (b) Compare this with the accepted value of 5.979 x 10^24 kg.

2. (a) Calculate the ratio r^3/T^2 for the moon's orbit about the earth, where r is the average radius and T is the period. Express the answer in SI units. (b) Calculate the same ratio for any moon of Jupiter. (c) Why are the answers not equal? (NOTE: do not use Newton's expression for this quantity, just use the raw numbers for period and radius, which you can easily find. Since you live in the age of the internet, I do not have to give you all the data required for homework. Spending 20 seconds with a search engine gives lots of web sites such as http://nssdc.gsfc.nasa.gov/planetary/factsheet/joviansatfact.html)

3. One of Jupiter's moons, Callisto, has a period of 16.69 days, and an orbital radius of 1.88 x 10^9 m. Find the mass of Jupiter from these data, and compare with the accepted mass of Jupiter (1.90 x 10^(27) kg).

4. Find the acceleration of gravity at an altitude above the earth's surface equal to 2 times the radius of the earth. (This is then 3 earth radii from the center of the earth.) You should not need to use the values for the earth's radius or mass, nor do you need G, the gravitational constant.

5. A geosynchronous satellite is in a circular orbit above the equator, with a radius of 6.63 times the earth's radius. If the satellite weighs 4.50 tons at the earth's surface, what is the force of gravity (in tons) on the satellite when it is in orbit? (You don't need to know values for the earth's radius or mass. Just use the fact that the force of gravity is inversely proportional to the square of the distance.)

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