Free Gravitation MCQs with Answers

151. An elevator initially accelerates upward from rest and then ascends with uniform speed. The time period of a simple pendulum in the elevator will:

• A. Increase and then decrease
• B. Decrease and then increase
• C. Increase
• D. Decrease

Explanation: In an elevator that initially accelerates upward from rest and then ascends with uniform speed, the effective gravitational force experienced by the simple pendulum inside the elevator will change. During the initial acceleration, the effective gravitational force will be greater than g. As a result, the time period of the simple pendulum will be shorter because the effective acceleration acting on the pendulum is greater. Once the elevator reaches a constant speed, the effective gravitational force will return to g, and the time period of the simple pendulum will return to its original value. Hence B is the correct option.

152. Assume the earth to be homogeneous. Scientist A goes deep down in a mine and Scientist B goes up in a balloon. The value of g measured by:

• A. Each goes on decreasing
• B. Each remains unaltered
• C. B goes on decreasing and that of A goes on increasing
• D. A goes on decreasing and that of B goes on increasing

Explanation: A is correct. The value of g decreases up to 0 as we go toward the center of the Earth, and it also decreases as we go away from the Earth's surface.

153. A man of weight w is standing on a lift which is moving upward with an acceleration a. The apparent weight of the man is:

• A. Option A
• B. Option B
• C. Option C
• D. Option D

Explanation: D is the correct option. As the body is moving upwards, 2 unbalanced forces are acting on the body, weight and the apparent weight (or the reaction force, R) causing the body to accelerate.

154. If a satellite of mass m, orbits around the Earth of mass Me, in an orbit of radius r, its angular speed will be:

• A. Option A
• B. Option B
• C. Option C
• D. Option D

Explanation: A is correct as per the derived formula by equating gravitational acceleration and centripetal acceleration. Angular speed is inversely proportional to the square root of the cube of radius.

155. If two masses 1 kg and 10 kg are 1 m apart, then acceleration of:

• A. Both masses is same
• B. 1 kg is greater than that of 10 kg
• C. 10 kg is greater that that of 1 kg
• D. Both masses is zero

Explanation: Gravitational acceleration on the mass of 1kg is = G x 10/12 =10 GSimilarly, gravitational acceleration on the mass of 10kg is = 1GHence it can be seen that 1kg mass accelerates 10 times more than the 10kg mass.

156. If the gravitational force between two identical masses m, is 6.67 x 10^-11 N, when they are 1 m apart, then the value of each mass will be:

• A. 2 kg
• B. 1 kg
• C. 0.5 kg
• D. 4 kg

Explanation: F=Gmm/R2 As F= 6.67 x10-11 N, it can be seen that F=G and this is only possible when the product of masses is equal to 1.This can also be seen by adding these values to the formula = F=G(1)(1)/12 Hence F=G and the correct option is B.

157. A mass of 100 kg in an elevator is descending with a = 1m/sec2. Its apparent weight will be:

• A. 1080 N
• B. 880 N
• C. 980 N
• D. 100 N

Explanation: As the escalator is descending downwards with some acceleration, the formula to calculate the apparent weight becomes = mg-maEntering the values given in calculation , W' =(100 x 9.81)-(100 x 1)W' = 881 NHence the correct option is B.

158. If the distance between two masses each 1kg, is 1m, then the force of attraction between the two will be:

• A. 9 x 10^9 N
• B. 6.67 x 10^-11 N
• C. 3 x 10^-11N
• D. 8.8 x 10^-12 N

Explanation: F=GMm/R2 As the distance and both the masses are equal to 1, F= G Where G is a universal gravitational constant with the value of 6.67 x 10-11 N .

159. The relation between the orbital speed v, of a planet and its orbital radius r, is:

• A. Option A
• B. Option B
• C. Option C
• D. Option D

Explanation: The orbital velocity is inversely proportional to the square root of the radius (considering G and M to be constants). Hence A is correct.

160. The acceleration due to gravity on a planet with mass and radius half of the Earth will be:

• A. 4.9 m/sec2
• B. 9.8 m/sec2
• C. 19.6 m/sec2
• D. 2.45 m/sec2

Explanation: Gravitational acceleration on Earth = GM/R2 Gravitational acceleration on another planet with mass and radius half = G(0.5M)/0.25R2 Comparing both the g, their ratio will be, g'/g= 2/1The value of g on Earth is 9.81m/s2, so the value of g' will be 9.81 x 2 =19.6m/s2.Hence the correct option is C.