MPSC State Service 2020 · CSAT · Question 21 of 77

Passage: Read the following passage and answer the questions. Physics Passage The general motion of a massive object under the influence of the Earth՚s gravitational force can be solved in closed form using Newton՚s second law. The gravitational force is given by: GmM e F = R2 Where G is the universal gravitational constant, m is the mass of the object, Me is the mass of the Earth and R is the distance of the object from the center of the Earth One result of this analysis is that Kepler՚s laws can be derived for satellites orbiting the Earth. These three laws were originally discovered by Johannes Kepler (1571 - 1630) based on observations of the motion of the planets about the Sun. They are as follows: (I) All satellites move in elliptical orbits with the Earth at one focus. (II) A line that connects a satellite to the center of the Earth sweeps out equal areas in equal times. (III) The square of the period of any satellite is proportional to the cube of the semimajor axis of its orbit. For objects near the surface of the Earth, a great simplification in the mathematics occurs by approximating the gravitational force to be a constant. Let R = Re + h, where Re is the radius of the Earth, h is distance of the object from earth surface. The gravitational force can now be written as: GmM e F = ( Re + h ) 2 GmM e Which is approximately equal to R e 2 when h ≪ Re. This constant force is usually set equal to mg, where g is defined to be the free-fall acceleration. 24 (Note: G = 6. 67 × 1 0 I N. m2/kg2. The mass of the Earth is Me = 5.98 × 10 kg and its radius is Re = 6.37 × 106 m) A satellite of mass m is in circular orbit around the Earth at a distance R from the Earth՚s center. If R is increased by a factor of 4, then the period of the orbit will be:

Reading Comprehension

1. Aunchanged
2. Bincreased by a factor of 4
3. Cincreased by a factor of 8Correct
4. Dincreased by a factor of 64