Test: Gravitation - UPSC MCQ

The reasoning behind this is that the force of gravity is weaker at higher altitudes compared to sea level. As you move higher up a mountain, you are farther away from the center of the Earth, which results in a slightly reduced gravitational pull. Since weight is the force exerted on an object due to gravity, the weight of the apple would decrease.

Therefore, if option A) decreased is considered correct, then the weight of an apple taken to the top of a mountain would decrease.

The gravitational force between two objects can be calculated using Newton's law of universal gravitation:

F = (G * m¹ * m²) / r²

Where: F is the gravitational force between the objects, G is the gravitational constant (approximately 6.673 × 10^-11 Nm²/kg²), m² and m² are the masses of the two objects, and r is the distance between their centers.

In this case, we have two lead spheres with masses of 1000 kg each, and their centers are 1 meter apart. Plugging these values into the formula, we get:

F = (6.673 × 10^-11 * 1000 * 1000) / 1²

F = 6.673 × 10^-11 * 10⁶

F = 6.673 × 10^-5

So, the gravitational force with which the lead spheres attract each other is approximately 6.673 × 10^-5 Newtons.

Therefore, the correct answer is option D) 6.673 × 10^-5.

According to Newton's law of universal gravitation, the force of gravitational attraction between two objects is inversely proportional to the square of the distance between their centers. Mathematically, it can be represented as:

F = G * (m1 * m2) / r²

Where:

• F represents the force of gravity between the two masses,
• G is the gravitational constant,
• m1 and m2 are the magnitudes of the masses of the objects, and
• r is the distance between the centers of the objects.

So, as the distance between the masses increases, the gravitational force between them decreases, following the inverse square relationship.

The value of the Universal Gravitational Constant (G) in CGS (Centimeter-Gram-Second) units is approximately 6.67 * 10^(-8) cm³ g^(-1) s^(-2).

So, the correct option from the provided choices is C) 6.67 * 10^(-8) cgs unit.

According to Newton's law of universal gravitation, every object with mass exerts an attractive force on every other object with mass. This gravitational force is always attractive, regardless of the distance between the objects. It decreases with distance, becoming weaker as the distance between the objects increases, but it is still attractive at all distances.

The gravitational force between two bodies is inversely proportional to the square of the distance between them. If the distance between two bodies becomes 6 times more than the usual distance, it means the new distance is 6 times the original distance.

The gravitational force is inversely proportional to the square of the distance, so if the distance becomes 6 times more, the gravitational force will be (1/6)² = 1/36 times the original force.

Therefore, the correct option is D) 1/36 times.

The weight of a body is slightly greater at the poles, so the correct option is A) At Polar region.

This is because the Earth is not a perfect sphere but is slightly flattened at the poles and bulges at the equator due to its rotation. As a result, the distance from the center of the Earth to a point at the poles is slightly shorter compared to the distance at the equator. Since weight is directly proportional to the distance from the center of the Earth, objects weigh slightly more at the poles than at the equator.

The weight of a body can be calculated using the formula:

Weight = Mass × Acceleration due to gravity

On the Moon's surface, the acceleration due to gravity is approximately 1.6 m/s², as given in the question. So, let's calculate the weight of a 100 kg body on the Moon's surface:

Weight = 100 kg × 1.6 m/s² = 160 N

Therefore, the correct option is D) 160 N.

As we go farther away from Earth, the gravitational force becomes weaker.

According to Newton's law of universal gravitation, the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

As the distance between two objects increases, the gravitational force decreases. Therefore, the correct option is C) weaker.

The statement "Every body in the universe attracts every other body with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers" is known as the law of gravitation.

Therefore, the correct option is B) law of gravitation. This law is derived from Newton's law of universal gravitation, which describes the gravitational interaction between two objects.