Free Gravitation MCQs with Answers

241. Value of escape velocity for the surface of the earth is 11 km/sec. Its value for surface of the moon is:

• A. 11 km/sec
• B. 10.4 km/sec
• C. 2.4 km/sec
• D. 4.3 km/sec

Explanation: The correct answer is Option C: 2.4 km/sec. The escape velocity for the Moon is approximately 2.374 km/sec. This is significantly lower than Earth's escape velocity due to the Moon's smaller mass and gravitational pull. Options A and B are incorrect because they refer to the escape velocities of Earth and Venus, respectively. Option D is also incorrect as it does not correspond to any known celestial body's escape velocity.

242. A moon rotates about its axis. In the future, scientists may wish to put a satellite into an orbit around the moon such that the satellite remains stationary above one point on moon surface, the period of rotation of moon about its axis is 27.4 days,what is the radius of required orbit? Mass of the moon =7.35x10²²kg

• A. 3.59 x 10^7 m
• B. 4.23 x 10^7 m
• C. 8.86 x 10^7 m
• D. 6.96 x 10^6 m

Explanation: In this case, once the satellite has been launched, the gravitational force between the satellite and the moon would be providing the centripetal force hence the centripetal force, mrw2 is equal to the gravitational force, GMm/r2 where r is the radius of the orbit, w being the angular velocity that can be simplified to 2π/T(time period) and M being the mass of the moon. Equating the two expressions would give us r= (GMT2/4π2)1/3 Plugging in all the values, performing mathematical operations and then finally taking cube root of the expression gives you the answer i.e 8.8x10⁷m

243. When the spaceship rotates with _ frequency, the artificial gravity like earth is produced to inhabitants of the ship

• A. 2π √ R / g
• B. 2π √ ℓ / g
• C. 1 / 2π √ R / g
• D. f ≥ √(g / r)

Explanation: Explanation:When a spaceship raotates, the centripetal force creates a sensation of artificial gravity on the spaceship's interior. The frequency of rotation required to produce this artificial gravity is given by the formula: f = 1/2π √(g/R)Where f is the frequency of rotation, g is the acceleration due to gravity, and R is the radius of the spaceship.

244. When a lift is accelerated upward, the apparent weight of an object in it will be:

• A. Equal to its real weight
• B. Less than its real weight
• C. Zero
• D. Greater than its real weight

Explanation: The apparent weight of an object is the force exerted by the object on the surface it is resting on. When a lift is accelerated upward, the acceleration adds to the gravitational pull, making the apparent weight greater than the real weight. This is due to the net force being the sum of gravitational force and upward acceleration. In contrast, if the lift were accelerating downward, the apparent weight would be less. If the lift were in free fall, the apparent weight would be zero because both the object and the lift would be accelerating at the same rate, eliminating any normal force.

245. A 100kg man is standing in an elevator, which accidentally falls freely. What will be the weight of the person in the freely falling elevator (take g=10 m/s^2)

• A. 1000 N
• B. 10 N
• C. 500 N
• D. Zero

Explanation: Being free fall, the man will be in a state of weightlessness As it is a numerical, it can have only one possible answer.

246. The value of G at the moon as compared with its value at the earth is :

• A. Smaller
• B. Same
• C. Greater
• D. Zero

Explanation: The gravitational constant G is a fundamental constant of nature that expresses the strength of gravitational attraction between two masses. It is a universal constant, meaning it remains the same throughout the universe. Thus, the value of G is the same on the Moon as it is on Earth, or anywhere else.Options A, C, and D are incorrect because they suggest G can vary based on location, which contradicts the definition and understanding of G as a universal constant.

247. A body weighs 72 kg on the surface of the earth its weights on the surface of the moon will be:

• A. 72 kg
• B. 12kg
• C. 24 kg
• D. 0kg

Explanation: The weight of an object on the surface of the moon can be calculated using the formula:Weight on the moon = Weight on the Earth× (Acceleration due to gravity on the moon / Acceleration due to gravity on the Earth)The acceleration due to gravity on the moon is about 1/6th of that on Earth.Weight on the moon = 72kg × (⅙)= 12kgTherefore, the weight of the body on the surface of the moon will be 12kg.

248. The dimensions of the gravitational constant are:

• A. [M2L2T]
• B. [M-1L3T-2]
• C. [M2L-2T-2]
• D. [ML-2T-1]

Explanation: The dimensions of the gravitational constant can be expressed using the equation for Newton's law of universal gravitation:F = Gm1m2 / r²By rearranging the equation, we can determine the dimensions of G:G = Fr² / m1m2The dimensions of the gravitational constant can be derived as follows:[Force] = [Mass][Acceleration]= [Mass][Length] / [Time]3Substituting the dimensions into the equation:G = ([M][L] / [T]²) × [L]² / [M][M]G = M-1L3T-2

249. The ratio of inertial mass to the gravitational mass is equal to:

• A. 1/2
• B. 1
• C. 2
• D. No fixed number

Explanation: Inertial mass is a measure of how fast an object accelerates--given the same force, increasing the inertial mass implies decreasing acceleration. The simplest way to state the equivalence principle is this: inertial mass and gravitational mass are the same thing.The inertial mass and gravitational mass of an object are identical in value, so their ratio is 1. They differ in how they are measured. Inertial mass is measured by measuring an object's resistance to changes in velocity; while gravitational mass describes the force on an object in a gravitational field.A, C, D: These options are incorrect as they do not state the true value of the ratio i.e. 1.

250. The escape velocity of body from a planet does not depend upon;

• A. The mass of a body
• B. The mass of the planet
• C. The average radius of the planet
• D. The density of the planet

Explanation: The escape velocity 'v' of a body depends upon the acceleration due to gravity of the planet and the radius of the planet but not on mass of planet.