Chapter 5: Work, Energy and Power Short Questions | physics Class 11 CBSE

ByteNotes

Chapter 5: Work, Energy and Power Short Questions | physics Class 11 CBSE | ByteNotes.in

Short Answer

Easy difficulty • Direct answer format

Easy

Question 1

Quick Recall

Define the scalar product of two vectors and state its geometrical interpretation.

The scalar product of two vectors A and B is defined as A·B = AB cos θ, where θ is the angle between the two vectors; the result is a scalar quantity.
Geometrically, A·B equals the magnitude of A multiplied by the projection of B onto A, or equivalently the magnitude of B multiplied by the projection of A onto B.
The scalar product is commutative (A·B = B·A) and distributive over vector addition: A·(B + C) = A·B + A·C.

ByteNotes

Short Answer

Easy difficulty • Direct answer format

Easy

Question 2

Quick Recall

State the three conditions under which no work is done by a force on an object.

No work is done when the displacement is zero; for example, a weightlifter holding a 150 kg mass steadily on his shoulder does no work on the load.
No work is done when the force is zero; for example, a block sliding on a smooth frictionless table has no horizontal force acting on it even if it undergoes displacement.
No work is done when force and displacement are mutually perpendicular (θ = 90°), since cos 90° = 0; the earth's gravitational force does no work on the moon if its orbit is assumed perfectly circular.

ByteNotes

Short Answer

Easy difficulty • Direct answer format

Easy

Question 3

Quick Recall

State the work-energy theorem and write its mathematical expression.

The work-energy theorem states that the change in kinetic energy of a particle is equal to the net work done on it by all the forces acting on it.
Mathematically, Kf − Ki = Wnet, where Ki is the initial kinetic energy, Kf is the final kinetic energy, and Wnet is the total work done by the net force.
This theorem is essentially a scalar form of Newton's second law and holds for both constant and variable forces in all inertial frames.

ByteNotes

Short Answer

Easy difficulty • Direct answer format

Easy

Question 4

Quick Recall

Explain why the work done by friction is always negative when an object slides over a surface.

Friction always opposes the direction of motion; the angle between the frictional force and the displacement of the object is always 180°.
Since W = Fd cos θ and cos 180° = −1, the work done by friction is W = −Fd, which is always a negative quantity.
This negative work reduces the kinetic energy of the object, causing it to decelerate and eventually come to rest, as demonstrated in the cyclist skidding example in the chapter.

ByteNotes

Short Answer

Easy difficulty • Direct answer format

Easy

Question 5

Quick Recall

Write the expression for kinetic energy and explain why it is always a positive quantity.

The kinetic energy of an object of mass m moving with velocity v is K = (1/2)mv², derived from the scalar product K = (1/2)m(v·v).
Mass m is always positive, and v² = v·v = |v|² cos 0° is the square of the speed, which is always non-negative regardless of the direction of motion.
Since both m and v² are non-negative, kinetic energy K is always a positive (or zero) scalar quantity, unlike work which can be positive, negative, or zero.

ByteNotes

Short Answer

Medium difficulty • Direct answer format

Medium

Question 6

Quick Recall

How is work done by a variable force calculated? Explain with reference to a force-displacement graph.

For a variable force F(x), the displacement is divided into infinitesimally small elements dx; over each element the force is approximately constant and the work done is dW = F(x) dx.
The total work done is obtained by integrating: W = ∫F(x) dx from xi to xf, which is the limit of the sum of all such small rectangular areas as Δx → 0.
On an F-x graph, the total work done by the variable force equals the area enclosed under the force-displacement curve between the initial and final positions.

ByteNotes

Short Answer

Medium difficulty • Direct answer format

Medium

Question 7

Quick Recall

Define potential energy and state the condition for a force to have an associated potential energy function.

Potential energy is the energy stored in a body by virtue of its position or configuration; it is released as kinetic energy when the body is free to move under the influence of the storing force.
A potential energy function V(x) can be defined for a force F(x) only if the force is conservative, i.e., the work done by the force depends only on the end points and not on the path taken.
Mathematically, F(x) = −dV/dx; the change in potential energy equals the negative of work done by the conservative force: ΔV = −F(x) Δx.

ByteNotes

Short Answer

Medium difficulty • Direct answer format

Medium

Question 8

Quick Recall

State the principle of conservation of mechanical energy and the condition under which it holds.

The principle states that the total mechanical energy (sum of kinetic energy K and potential energy V) of a system remains constant throughout the motion.
This principle holds only when all forces doing work on the system are conservative forces; non-conservative forces like friction violate this principle.
Mathematically, Ki + Vi = Kf + Vf, or equivalently ΔK + ΔV = 0 and Δ(K + V) = 0 at every point in the motion.

ByteNotes

Short Answer

Easy difficulty • Direct answer format

Easy

Question 9

Quick Recall

State Hooke's law for a spring and write the expression for the potential energy stored in a stretched spring.

Hooke's law states that the spring force Fs is proportional to the displacement x from the equilibrium position and directed opposite to it: Fs = −kx, where k is the spring constant in N m⁻¹.
The spring is described as stiff if k is large and soft if k is small; the negative sign indicates that the spring force always acts to restore the block to equilibrium.
The potential energy stored in a spring displaced by x from equilibrium is V(x) = (1/2)kx², which is always positive and has its minimum (zero) value at the equilibrium position x = 0.

ByteNotes

Short Answer

Easy difficulty • Direct answer format

Easy

Question 10

Quick Recall

Define power and write its SI unit. How is instantaneous power related to force and velocity?

Power is defined as the time rate at which work is done or energy is transferred; average power Pav = W/t and instantaneous power P = dW/dt.
The SI unit of power is the watt (W), equal to 1 joule per second (1 J s⁻¹), named after James Watt; another unit is horsepower where 1 hp = 746 W.
Instantaneous power is related to force and velocity by P = F·v, where v is the instantaneous velocity and F is the instantaneous force; power is a scalar quantity with dimensions [ML²T⁻³].

ByteNotes

Short Answer

Medium difficulty • Direct answer format

Medium

Question 11

Quick Recall

Distinguish between elastic and inelastic collisions on the basis of kinetic energy conservation.

In an elastic collision, both total linear momentum and total kinetic energy of the system are conserved; the kinetic energy before and after the collision remains the same.
In an inelastic collision, total linear momentum is conserved but total kinetic energy is not conserved; some kinetic energy is converted into heat, sound, or deformation energy during collision.
A completely inelastic collision is a special case where the two bodies stick together and move as one unit after collision, resulting in the maximum possible loss of kinetic energy consistent with momentum conservation.

ByteNotes

Short Answer

Medium difficulty • Direct answer format

Medium

Question 12

Quick Recall

In a one-dimensional elastic collision between equal masses, what happens to the velocities of the two bodies after collision?

When two equal masses m1 = m2 undergo a one-dimensional elastic collision with m2 initially at rest, applying conservation of momentum and kinetic energy gives v1f = 0 and v2f = v1i.
The first (moving) mass comes to a complete stop and the second (stationary) mass moves forward with exactly the initial speed of the first mass.
This result demonstrates a complete transfer of both momentum and kinetic energy from the first body to the second, a result seen in games like billiards and the Newton's cradle demonstration.

ByteNotes

Short Answer

Medium difficulty • Direct answer format

Medium

Question 13

Quick Recall

Why is the gravitational force considered a conservative force? Give two properties.

The gravitational force is conservative because the work done by it depends only on the initial and final heights of the object and not on the path taken between them.
An object of mass m released from rest on a smooth frictionless inclined plane of height h reaches the bottom with speed √(2gh), irrespective of the angle of inclination, confirming path independence.
Additionally, the work done by gravity over any closed path is zero; if an object returns to its starting height, the net work done by gravity is zero, satisfying the definition of a conservative force.

ByteNotes

Premium Access

Unlock all Short Questions

You are viewing 13 free short questions from this chapter. Upgrade to Premium to unlock the remaining 12 questions.

Upgrade to Premium12 questions locked

Chapter sections

Chapter 5: Work, Energy and Power | Short Questions

Define the scalar product of two vectors and state its geometrical interpretation.

State the three conditions under which no work is done by a force on an object.

State the work-energy theorem and write its mathematical expression.

Explain why the work done by friction is always negative when an object slides over a surface.

Write the expression for kinetic energy and explain why it is always a positive quantity.

How is work done by a variable force calculated? Explain with reference to a force-displacement graph.

Define potential energy and state the condition for a force to have an associated potential energy function.

State the principle of conservation of mechanical energy and the condition under which it holds.

State Hooke's law for a spring and write the expression for the potential energy stored in a stretched spring.

Define power and write its SI unit. How is instantaneous power related to force and velocity?

Distinguish between elastic and inelastic collisions on the basis of kinetic energy conservation.

In a one-dimensional elastic collision between equal masses, what happens to the velocities of the two bodies after collision?

Why is the gravitational force considered a conservative force? Give two properties.

Unlock all Short Questions