The gravitational force exerted by the planet Earth on a unit mass at a distancer from the center of the planet is GMr if rR where M is the mass of Earth, Ris its radius, and G is the gravitational constant. Is F a continuous function of r?

(a) Compute the mass of the earth from knowledge of the earth-moon distance (3.84 * 10^8 m) and of the lunar period (27.3 days). (b) Then calculate the average density of the earth. The average radius of the earth is 6.38 * 10^6 m.

Suppose you could pack neutrons (mass = 1.67 × 10-27 kg) inside a small ball of radius 0.026 m in the same way as neutrons and protons are packed together in the nucleus of an atom. (a) Approximately how many neutrons would fit inside the ball? (b) A small object is placed 3.7 m from the center of the neutron-packed ball, and the ball exerts a gravitational force on it. When the object is released, what is the magnitude of the acceleration that it experiences? Ignore the gravitational force exerted on the object by the earth.

The mean diameters of Mars and Earth are 6.9×10^3km and1.3×10^4km, respectively. The mass of Mars is 0.11 timesEarth's mass [Mass of Earth = 5.98×10^24kg]. What is: a)The ratio of the mean density (mass per unit volume) of Mars to that of Earth? b)The value of the gravitational acceleration on Mars? c)The escape speed on Mars?

A high tech company uses a satellite to measure the size of features on the surface of the earth. They use this technology to measure a particular rectangular field and find it's length to be 444 ± 1.8 in meters and it's width to be 198 ± 1.63 in meters. They plan to report the perimeter (sum of two lengths and two widths) of the field as P± SP in units of yards. (1 meter = 1.094 yards) What is SP?

An ant crawls on the surface of a ball of radius b in such a manner that the ant's motion is given in spherical coordinates by the equations r = b; phi = omega*t; theta = pi/2 * [1 + 1/4 * cos(400t)] Find the speed of the ant as a function of the time t. What sort of path is represented? by the above equations ?

Using spherical polar coordinates r, 0, p to find CM of a uniform solid hemisphere of radius R, whose flat face lies in the xy plane with its center at the origin. The element of volume is in spherical polars of dV = r² dr sine de dip.

A rectangle expands and contracts with time t (in seconds). Its area is given by A= 4 + sin t square meters. At t = 3.14 (pi), the following is observed. (1) the width of the rectangle expands at the rate of 0.1 meters per second. (2) The width of the rectangle is 1 meter long How fast is the height of the rectangle changing at t = 3.14 (pi)?

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The gravitational force exerted by the earth on a unit massat a distance r from the center of the planet is   where M is the mass of the earth,R is its radius, and G isthe gravitational constant. Is F a continuous function of r ?