Free Gravitation MCQs with Answers

201. A man whose weight is 900 N on the earth's surface goes to a height, which is equal to twice the earth's radius, above the surface of the earth, then the new weight of the man will be:

• A. 900 N
• B. 225 N
• C. 300 N
• D. 100 N

Explanation: The following is the solution:Weight of object on earth W=GMm/r2Now, M=ρV =4πρR3/3∴W=GρπR3Gm/3R2=4πρRGm/3WP/WE=(ρP/ρE)(RP/RE)WP=900/12=75N

202. An object is taken from the earth to a planet where the value 'g' is 20 m/s2, if it is compared with value of 'g' earth, which of the following statement is true?

• A. Weight at the planet will be greater
• B. Weight at the Earth will be greater
• C. Mass at the planet will be greater
• D. Mass at the planet will be smaller

Explanation: This is more likely to be true. If the value of g on the planet is 20 m/s², and on Earth, it is approximately 9.8 m/s², then the weight on Earth would be greater because W=mg, and the mass (m) remains constant.

203. What is minimum energy required to launch a satellite of mass m from the surface of a planet of mass m and radius r in a circular orbit at an altitude 2R:

• A. 2GmM/3R
• B. GmM/2R
• C. GmM/3R
• D. 5GmM/6R

Explanation: To solve this problem, we can use the concept of gravitational potential energy. The potential energy of an object due to gravity is given by:PE = -G * M * m / rwhere:G is the gravitational constantM is the mass of the planetm is the mass of the satelliter is the distance between the center of the planet and the satelliteIn this scenario, we need to consider the initial and final potential energies of the satellite:Initial potential energy (PE_i): When the satellite is at the surface of the planet (r = R), its potential energy is:PE_i = -G * M * m / RFinal potential energy (PE_f): When the satellite reaches the circular orbit at an altitude of 2R (r = 3R), its potential energy is:PE_f = -G * M * m / (3R)Escape velocity: The minimum energy required to launch the satellite and overcome the gravitational pull of the planet is known as the escape velocity (v_e). It can be calculated using the following equation:1/2 * m * v_e^2 = -G * M * m / RSolving for v_e, we get:v_e = sqrt( 2 * G * M / R )Kinetic energy (KE): Once the satellite reaches the circular orbit, it needs to have enough kinetic energy to maintain its orbital motion. This kinetic energy can be calculated using the following equation:KE = 1/2 * m * v^2where v is the orbital velocity of the satellite.Total energy (E): The minimum total energy required (E) is the sum of the escape velocity and the kinetic energy needed for the orbit:E = KE + PE_f = 1/2 * m * v^2 - G * M * m / (3R)Relating orbital velocity and escape velocity: In a circular orbit, the orbital velocity (v) is related to the escape velocity (v_e) by:v = v_e / sqrt(2)Substituting this relationship into the equation for total energy:E = 1/2 * m * (v_e^2 / 2) - G * M * m / (3R)Simplifying the equation:E = (1/4) * G * M * m / R - G * M * m / (3R)Combining terms:E = ( -3G * M * m + G * M * m ) / (12R)This simplifies to:E = 5GmM / 6RTherefore, the minimum energy required to launch the satellite (5GmM/6R) corresponds to option d in the question

204. According to Einstein, the gravity interaction is possible between

• A. Material object only
• B. Both material objects and electromagnetic radiation
• C. Electromagnetic radiations only
• D. none of these

Explanation: Reason: According to Einstein's general theory of relativity, gravity is not just a force between masses but is also the result of the curvature of spacetime caused by the presence of mass and energy, including

205. In the solar eclipse of 1919 A.D., bending of starlight was measured to be

• A. 1.745 degree
• B. 1.745 minutes
• C. 1.745 seconds
• D. 1.745 radians

Explanation: The bending of starlight during the solar eclipse of 1919 was measured to be approximately 1.745 degrees, supporting Einstein's theory of general relativity.

206. If OE is the angle of bending of light predicted by Einstein's theory of gravity and ON that by Newton's, then

• A. OE= ON
• B. OE= 0.5 ON
• C. OE =2ON
• D. No relation exists between OE and ON

Explanation: The angle of bending of light predicted by Einstein's theory is approximately double that predicted by Newton's theory. Therefore, OE = 2ON.

207. Time taken by a geostationary satellite to complete one rotation around the Earth is

• A. 1 year
• B. 1 day
• C. 1 hr
• D. 84 min

Explanation: A geostationary satellite orbits the Earth once every 24 hours, which is the same time it takes for the Earth to complete one rotation. This ensures that the satellite remains above the same point on the Earth's surface.

208. The Global Positioning System (GPS) consists of how many satellites?

• A. 24 Natural satellites
• B. 4 Natural satellites
• C. 3 Synchronous satellites
• D. both and and b

Explanation: The GPS consists of a constellation of 24 satellites in orbit around the Earth.

209. A satellite moving round the Earth constitutes

• A. An inertial frame of reference
• B. A non-inertial frame of reference
• C. Neither inertial nor non-inertial
• D. both inertial and non inertial

Explanation: A satellite orbiting the Earth is continuously accelerating toward the Earth (centripetal acceleration due to gravity). A frame undergoing acceleration is non-inertial, so the satellite constitutes a non-inertial frame of reference (option B).

210. INTELSAT has the capacity of

• A. 3 channels
• B. 30,000 two-way telephone
• C. 50,000 two-way telephone
• D. both (a) & (b)

Explanation: INTELSAT, or the International Telecommunications Satellite Organization, provides various communication services, including telephone, television, and data transmission. It has the capacity for thousands of telephone channels and other communication services.