This problem involves the concept of static equilibrium. For a beam to be in static equilibrium, two conditions must be met: the sum of all vertical forces must be zero, and the sum of all moments about any point must be zero. Given that the beam is uniform and the weight is placed exactly at its center, symmetry plays a crucial role in determining the reaction forces at the supports.
A) Equal at both ends — Due to the uniform nature of the beam and the weight being placed precisely at its center, the loading is symmetrical, leading to an equal distribution of the load to both supports. This is confirmed by applying the principles of static equilibrium (sum of forces and sum of moments equal zero).
This question tests the understanding of different types of equilibrium: stable, unstable, and neutral. We need to recall the definition of neutral equilibrium and how an object behaves when slightly displaced from such a state.
Correct Option: B) Remain in its new position after displacement
The question asks for the definition of the moment of force, also known as torque. We need to recall the fundamental formula for torque in physics.
Where:
Comparing this definition with the given options, option A aligns perfectly with this understanding.
A) Force multiplied by the distance from the point of rotation
This option correctly defines the moment of force (torque) as the product of the applied force and the perpendicular distance (lever arm) from the axis of rotation to the point where the force is applied. This product quantifies the rotational effect of the force.
This question tests the fundamental condition for rotational equilibrium. Rotational equilibrium occurs when an object is either at rest or rotating at a constant angular velocity. This state is governed by Newton's second law for rotation, which relates the net torque to the angular acceleration.
A) Zero — For an object to be in rotational equilibrium, the net torque acting on it must be zero. This ensures that there is no change in its angular velocity, meaning it either remains stationary or continues to rotate at a constant angular velocity. This condition holds true regardless of the point about which the moments are calculated.
A body will be in stable equilibrium if its potential energy:
Decreases with a slight displacement
Increases with a slight displacement
Remains unchanged with a slight displacement
Depends on the material of the body
The concept of equilibrium for a body is directly related to its potential energy. A body is in stable equilibrium if, when slightly displaced from its equilibrium position, it tends to return to that position. This behavior is determined by how its potential energy changes with displacement.
B) Increases with a slight displacement
In stable equilibrium, the potential energy of the body is at a local minimum. If the body is slightly displaced from this position, its potential energy will increase. This increase in potential energy creates a restoring force that acts to bring the body back to its original equilibrium position, which is the definition of stable equilibrium.
This question asks about the condition for neutral equilibrium of a body. Equilibrium refers to the state where the net force and net torque on an object are zero. There are three types of equilibrium: stable, unstable, and neutral. Each type is defined by how the center of gravity (CG) relates to the point of support or pivot.
C) The center of gravity should coincide with the point of support. This is the definition of neutral equilibrium. A classic example is a sphere resting on a flat surface; if you roll it, its center of gravity remains at the same height, and it stays in its new position.