The correct answer is: C. remains unchanged.
The weight of an object is the force of gravity acting on it. The force of gravity is proportional to the mass of the object and the acceleration due to gravity. The acceleration due to gravity is the same everywhere on Earth’s surface, so the weight of an object does not change if the Earth’s rotation speed changes.
However, the centrifugal force acting on an object does change if the Earth’s rotation speed changes. The centrifugal force is an apparent force that acts on objects that are moving in a circle. The centrifugal force is directed away from the center of the circle. The magnitude of the centrifugal force is proportional to the square of the object’s speed and the radius of the circle.
If the Earth’s rotation speed increases, the centrifugal force acting on objects on the Earth’s surface will increase. This is because the radius of the circle that objects on the Earth’s surface are moving in will decrease. The increase in the centrifugal force will cause objects to feel lighter. However, the increase in the centrifugal force will be very small, so the change in the weight of an object will be very small.
In conclusion, the weight of an object remains unchanged if the Earth’s rotation speed changes. However, the centrifugal force acting on an object will increase if the Earth’s rotation speed increases. This will cause objects to feel lighter.