Test: Universal Law Of Gravitation - Class 9 MCQ

The value of g, or gravity, varies based on location:

• It is greater at the poles due to the Earth's shape and rotation.
• The gravitational pull is maximum at the poles.
• As one moves towards the equator, the value of g decreases.

Weight of an object is highest at:

The weight of an object varies depending on its location due to the gravitational force exerted by the Earth. Here are the key points regarding why weight is highest at the poles:

• The gravitational force is influenced by the mass of the Earth and the distance from its centre.
• At the poles, the distance to the Earth's centre is shortest.
• This shorter distance results in a stronger gravitational pull, leading to a greater weight.
• In contrast, at the equator, the distance is greater, resulting in a slightly lower weight.

Therefore, an object weighs the most at the poles due to the stronger gravitational attraction.

Apple falls towards the earth, but the earth does not move towards the apple because

The reason for this phenomenon lies in the concept of acceleration and mass:

• The acceleration of an object is inversely proportional to its mass.
• The mass of the earth is significantly larger than that of an apple.
• As a result, the earth experiences a negligible acceleration towards the apple.
• This is why we observe the apple falling while the earth remains stationary.

To find the mass of a body with a weight of 59 N:

We can use the formula:

• Weight (W) = Mass (m) × Acceleration due to gravity (g)
• Given: W = 59 N and g = 9.8 m/s²

Rearranging the formula to find mass:

• m = W / g
• m = 59 N / 9.8 m/s²
• m ≈ 6.02 kg

Thus, the mass of the body is approximately 6 kg.

For vertically upward motion:

• The acceleration due to gravity, g, is negative as it opposes the motion.
• The equation for velocity is: v = u - gt
• At the peak height, the velocity is zero: 0 = u - gt
• From this, we find: t = u/g (1)

For vertically downward motion:

• Here, g is positive as it acts in the direction of motion.
• The equation for velocity is: v = u + gt
• At the moment of falling, the initial velocity is zero: v = 0 + gt
• Thus, we have: t = v/g (2)

By equating the time from equations (1) and (2), we find:

• v = u

Weight of a body on Earth is 48 N; its weight on the Moon is:

The weight of an object on the Moon can be calculated using the fact that the acceleration due to gravity on the Moon is approximately 1/6 that of Earth. Therefore, the weight on the Moon is:

• Weight on Earth: 48 N
• Weight on Moon: 48 N / 6
• Result: 8 N

Thus, the weight of the body on the Moon is 8 N.

A mass of 60 kg on Earth remains 60 kg on the Moon. This is because mass does not change regardless of location.

However, the weight of the object differs due to the gravitational pull:

• On Earth, the weight is calculated as:
• Weight on Earth = mass × gravity = 60 kg × 9.8 m/s² = 588 N
• On the Moon, the weight is:
• Weight on Moon = mass × gravity = 60 kg × 1.6 m/s² = 96 N

In summary:

• Mass remains constant at 60 kg.
• Weight on Earth is 588 N.
• Weight on the Moon is 96 N.

The value of acceleration due to gravity at the poles

The acceleration due to gravity varies between the poles and the equator:

• The effective gravity at the poles is approximately 9.832 m/s².
• At the equator, it is about 9.780 m/s².
• This means an object weighs about 0.5% more at the poles than at the equator.

Thus, the value of gravity is greater at the poles due to the combination of the Earth's shape and its rotation.

Gravitational force can be described by the formula:

F = G * (m₁ * m₂) / r²

• G is the gravitational constant.
• m₁ and m₂ are the masses of the two objects.
• r is the distance between the centres of the two masses.

From this formula, we can see that:

• The gravitational force is inversely proportional to the square of the distance (r).
• This means that as the distance increases, the gravitational force decreases.

Solution:

The gravitational force between the Earth and a 10 kg object can be calculated using the formula:

• F = m × g

Where:

• F is the gravitational force.
• m is the mass of the object (10 kg).
• g is the acceleration due to gravity (approximately 9.8 N/kg).

Substituting the values:

• F = 10 kg × 9.8 N/kg
• F = 98 N

Therefore, the magnitude of the gravitational force is 98 N.