Test: Work, Energy and Power - SSC CGL MCQ

The correct formula to calculate the work done by a constant force is W = Fs cos θ, where F is the force applied on a body, s is the displacement of the body, and θ is the angle between the force and the displacement vectors. This formula highlights the scalar nature of work and shows that work done is positive when the angle between the force and displacement is acute, and negative when the angle is obtuse.

The work done by a force is zero under two main conditions: when the body is not displaced (s = 0) and when the body is displaced perpendicular to the direction of the force (θ = 90°). In these scenarios, the force applied does not contribute to the work done on the body.

The work done by a variable force is represented by the area under the force-displacement graph. This relationship indicates that the work done is directly related to the area enclosed by the force-displacement curve. By calculating this area, one can determine the total work done by the force on the object.

Kinetic Energy is the energy a body possesses by virtue of its motion. It is dependent on the mass of the body and its velocity. When an object is in motion, it has kinetic energy. This form of energy is crucial in various phenomena, from simple movements to complex systems like vehicles in motion or celestial bodies orbiting in space.

According to Einstein's mass-energy relation, the energy produced when a mass Δm disappears is given by the equation E = Δmc². This famous equation, E=mc², signifies the equivalence of mass and energy. It states that mass can be converted into energy and vice versa, highlighting the profound interrelation between matter and energy in the universe.

Conservative forces in physics are non-dissipative forces, such as gravitational and electrostatic forces. One key characteristic of conservative forces is that the total mechanical energy initially is equal to the total mechanical energy finally in a system. This principle is derived from the law of conservation of energy, which states that energy cannot be created or destroyed, only transformed from one form to another.

In physics, power is defined as the rate at which work is done by a body. It represents the amount of energy transferred or converted per unit time. For instance, a 60-watt light bulb converts electrical energy into light and heat at a rate of 60 joules per second. This concept helps us understand how fast energy is being transformed or transferred, crucial in various practical applications like engineering and mechanics.

The SI unit of power is the watt, symbolized as "W." One watt is equivalent to one joule per second. This unit is commonly used to measure the rate of energy transfer, as in electrical systems, where the power rating of devices like light bulbs, motors, and heaters is specified in watts. Understanding this unit helps in quantifying and comparing the energy consumption or output of different devices accurately.

Power in physics is related to force and velocity by the equation P = F * v * cos(θ), where P is power, F is force, v is velocity, and θ is the angle between the force and velocity vectors. This relationship highlights that power is influenced by both the magnitude of the force applied and the speed at which an object moves in the direction of that force. Understanding this connection is crucial in analyzing mechanical systems and optimizing energy transfer efficiencies.

A collision involves particles interacting over a short duration with strong forces. In an elastic collision, both momentum and kinetic energy are conserved, indicating that all forces involved are conservative. On the other hand, in an inelastic collision, only momentum is conserved, and kinetic energy is not conserved. This distinction is crucial in understanding the behavior of colliding bodies and the effects of different collision types.

In a perfectly inelastic collision, the colliding bodies stick together after the collision and move with a common velocity. This type of collision conserves momentum but not kinetic energy, resulting in the loss of kinetic energy that is not recovered. The concept of perfectly inelastic collisions is essential in understanding how energy is transformed and dissipated during certain types of physical interactions.

The centre of mass of a physical system is a crucial point that describes the system's motion as a whole, behaving as if all the mass were concentrated at that point. This point moves in response to external forces, reflecting the overall mass distribution and motion of the system. Understanding the centre of mass is fundamental in analyzing the dynamics and behavior of complex physical systems.

The moment of inertia of a body about an axis of rotation is the sum of the products of the masses of its particles and the squares of their respective distances from the axis of rotation. This concept helps us understand how the mass of an object is distributed relative to its axis of rotation, influencing its rotational motion.

The theorem of parallel axes states that the moment of inertia about any parallel axis is the sum of the moment of inertia about the center of mass and the product of the mass and the square of the distance between the two axes. This theorem is crucial in calculating the moment of inertia of complex objects with respect to different axes.

The radius of gyration is the distance from the axis of rotation at which the total mass of the body can be considered to be concentrated, such that its moment of inertia remains the same. This concept simplifies calculations by allowing us to treat the mass distribution of a body as if it were concentrated at a single point while preserving its moment of inertia.