1. In mechanics, work is done on a body only when the applied force has a component along the body's displacement. Which situation shows mechanical work being done?
ⓐ. A person holds a bag while the bag remains at rest
ⓑ. A hand presses a wall while the wall remains fixed
ⓒ. A book is supported by a table while staying at rest
ⓓ. A force pushes a box so the box moves with the push
Correct Answer: A force pushes a box so the box moves with the push
Explanation: Mechanical work needs both force and displacement. A force alone is not enough if the point of application does not move in the direction of that force. When a box is pushed and it moves in the direction of the push, the force has a component along displacement, so work is done. Holding a bag at rest may require muscular effort, but the bag has no displacement, so mechanical work on the bag is zero. The key distinction is between everyday tiredness and mechanical work defined through force and displacement.
2. A person holds a heavy suitcase at a fixed height for several seconds. In the elementary mechanical sense, the work done on the suitcase by the person's upward force is
ⓐ. positive because the upward force is non-zero
ⓑ. negative because the suitcase has weight
ⓒ. zero because the suitcase has no displacement
ⓓ. equal to force multiplied by holding time
Correct Answer: zero because the suitcase has no displacement
Explanation: Work in mechanics is connected with displacement of the point on which force acts. The person applies an upward force on the suitcase, but the suitcase remains at the same position. Since displacement is zero, the mechanical work done on the suitcase by that force is zero. The force may balance the weight, but balancing a force is not the same as doing work. A force can exist without transferring mechanical energy through work.
3. Which description best captures the meaning of energy in mechanics?
ⓐ. Energy is the same physical quantity as force
ⓑ. Energy is the direction in which a body moves
ⓒ. Energy exists only during acceleration
ⓓ. Energy is the capacity to do work
Correct Answer: Energy is the capacity to do work
Explanation: Energy is commonly described as the capacity to do work. A moving body has kinetic energy, while a raised body or stretched spring can have potential energy because of its position or configuration. Energy is not the same physical quantity as force, since force is an interaction while energy is a scalar measure associated with doing work or causing change. A body can have energy even when it is not accelerating, such as a stone held at a height. The word capacity here means the body or system can produce work under suitable conditions.
4. Two machines lift identical loads through the same vertical height, but machine \(X\) completes the task in less time than machine \(Y\). The quantity that is definitely greater for machine \(X\) is
ⓐ. average power
ⓑ. mass lifted
ⓒ. displacement of the load
ⓓ. work done against gravity
Correct Answer: average power
Explanation: Both machines lift identical loads through the same height, so the work done against gravity is the same. Power compares how quickly work is done or energy is transferred. If the same work is completed in a shorter time, the average power is greater. The mass and vertical displacement are given to be identical, so they cannot explain the difference. This situation separates work from power: equal work can correspond to unequal power when the time taken is different.
5. Match the basic symbols with their usual meanings in work-energy-power notation.
| Symbol | Meaning |
|---|
| P. \(W\) | 1. kinetic energy |
| Q. \(K\) | 2. power |
| R. \(U\) | 3. work |
| S. \(P\) | 4. potential energy |
ⓐ. P-1, Q-3, R-4, S-2
ⓑ. P-3, Q-4, R-1, S-2
ⓒ. P-2, Q-1, R-4, S-3
ⓓ. P-3, Q-1, R-4, S-2
Correct Answer: P-3, Q-1, R-4, S-2
Explanation: The symbol \(W\) is commonly used for work. The symbol \(K\) represents kinetic energy, the energy associated with motion. The symbol \(U\) represents potential energy, the energy associated with position or configuration. The symbol \(P\) represents power, the rate of doing work or transferring energy. Keeping these symbols distinct prevents confusion between work \(W\) and power \(P\), even though both are closely related through time.
6. A bag is lifted slowly from the floor to a shelf. During this lifting process, the work done by the lifting force mainly increases the bag's
ⓐ. electric charge stored in the bag
ⓑ. thermal energy of the bag only
ⓒ. translational kinetic energy only
ⓓ. gravitational potential energy
Correct Answer: gravitational potential energy
Explanation: When a bag is lifted upward, its position in Earth's gravitational field changes. If it is lifted slowly, its speed need not increase much, so the main mechanical change is in gravitational potential energy. The lifting force transfers energy to the bag-Earth system through work. This is different from merely holding the bag at rest, where no displacement occurs. The useful idea is that work can transfer energy into stored mechanical form, not only into visible speed.
7. A car moving on a road is brought to rest by braking. In a simple mechanical description, the brakes and road forces reduce the car's
ⓐ. kinetic energy
ⓑ. mass
ⓒ. gravitational field strength
ⓓ. height above the road
Correct Answer: kinetic energy
Explanation: A moving car has kinetic energy because of its motion. During braking, forces opposing the motion do negative work on the car. This reduces the car's speed and therefore reduces its kinetic energy. The mass of the car is not normally reduced by braking in this mechanical model. The lost mechanical energy is transferred into other forms such as thermal energy in the brakes and tyres.
8. A runner climbs the same staircase twice, once slowly and once quickly. The work done against gravity is nearly the same in both climbs, but the quick climb has greater
ⓐ. displacement
ⓑ. weight of the runner
ⓒ. power
ⓓ. height gained
Correct Answer: power
Explanation: For the same runner and the same staircase, the gain in height is the same. The work done against gravity is therefore nearly the same in both climbs. Power depends on the time rate of doing work, so finishing the same climb in less time means greater power. This does not require a larger height or larger weight. The comparison shows why power describes how fast energy is transferred, while work describes the amount transferred.
9. Work and energy share the same SI unit because
ⓐ. both are vector quantities
ⓑ. power and energy are identical quantities
ⓒ. displacement and energy have the same dimensions
ⓓ. work is a mode of energy transfer
Correct Answer: work is a mode of energy transfer
Explanation: Work is one way by which energy is transferred to or from a body or system. Since work measures energy transferred, work and energy are measured in the same SI unit. That unit is the joule, written as \( \text{J} \). Power is not the same as energy because power includes the time rate of transfer. The shared unit of work and energy reflects their physical connection, not equality with power.
10. The relation \(1\,\text{J}=1\,\text{N m}\) means that one joule is the work done when
ⓐ. a force of \(1\,\text{N}\) moves a point \(1\,\text{m}\) along the force
ⓑ. a force of \(1\,\text{N}\) acts for \(1\,\text{s}\) with no stated displacement
ⓒ. a \(1\,\text{kg}\) body moves with speed \(1\,\text{m s}^{-1}\)
ⓓ. a power of \(1\,\text{W}\) acts through a distance of \(1\,\text{m}\)
Correct Answer: a force of \(1\,\text{N}\) moves a point \(1\,\text{m}\) along the force
Explanation: The unit relation \(1\,\text{J}=1\,\text{N m}\) comes from work done by a force along a displacement. If a force of \(1\,\text{N}\) moves its point of application by \(1\,\text{m}\) in the direction of the force, the work done is \(1\,\text{J}\). The factor "along its direction" matters because work depends on the component of force along displacement. A force acting for time alone does not define work unless displacement is also involved. The unit \( \text{N m} \) is a work or energy unit here, not a power unit.
11. The dimensions of work and energy are obtained from force multiplied by displacement. The dimensional formula is
ⓐ. \([MLT^{-2}]\)
ⓑ. \([ML^2T^{-1}]\)
ⓒ. \([M^2LT^{-2}]\)
ⓓ. \([ML^2T^{-2}]\)
Correct Answer: \([ML^2T^{-2}]\)
Explanation: Work has the form force multiplied by displacement when the force is along the displacement. The dimension of force is \([MLT^{-2}]\). The dimension of displacement is \([L]\). Multiplying them gives \([MLT^{-2}]\times[L]=[ML^2T^{-2}]\). Energy has the same dimensions as work because work measures energy transfer.
12. Study the table and identify the row that gives a mismatched SI unit.
| Row | Quantity | SI unit |
|---|
| P | Work | \(\text{J}\) |
| Q | Energy | \(\text{J}\) |
| R | Power | \(\text{W}\) |
| S | Force | \(\text{J}\) |
ⓐ. Row P
ⓑ. Row Q
ⓒ. Row S
ⓓ. Row R
Correct Answer: Row S
Explanation: Work and energy are both measured in joule, \( \text{J} \), so rows P and Q are matched correctly. Power is measured in watt, \( \text{W} \), so row R is also correct. Force is measured in newton, \( \text{N} \), not joule. The joule is related to force through \(1\,\text{J}=1\,\text{N m}\), but that does not make \( \text{J} \) the unit of force. The factor \( \text{m} \) in \( \text{N m} \) is essential because work includes displacement.
13. Work and energy are treated as scalar quantities in elementary mechanics. This means that their values
ⓐ. do not require a direction in space
ⓑ. must always be positive
ⓒ. must always be zero for circular motion
ⓓ. are measured only in \( \text{W} \)
Correct Answer: do not require a direction in space
Explanation: A scalar quantity is described by magnitude and sign where needed, but it does not have a direction in space like a vector. Work and energy are scalar quantities in elementary mechanics. Work can be positive, negative, or zero depending on the relation between force and displacement. Energy is also scalar, and many forms of mechanical energy are measured in joule, \( \text{J} \). A negative value of work is not a direction; it shows that energy is being removed from the motion or system under the chosen description.
14. A motor does \(120\,\text{J}\) of work in \(6\,\text{s}\). What is its average power?
ⓐ. \(12\,\text{W}\)
ⓑ. \(60\,\text{W}\)
ⓒ. \(720\,\text{W}\)
ⓓ. \(20\,\text{W}\)
Correct Answer: \(20\,\text{W}\)
Explanation: \( \textbf{Given:} \) Work done, \(W=120\,\text{J}\).
\( \textbf{Given time:} \) \(t=6\,\text{s}\).
\( \textbf{Required:} \) Average power of the motor.
\( \textbf{Relation:} \)
\[
P_{\text{avg}}=\frac{W}{t}
\]
This relation applies because average power is the rate at which work is done over the given time interval.
\( \textbf{Substitution:} \)
\[
P_{\text{avg}}=\frac{120\,\text{J}}{6\,\text{s}}
\]
\( \textbf{Calculation:} \)
\[
P_{\text{avg}}=20\,\text{J s}^{-1}
\]
Since \(1\,\text{W}=1\,\text{J s}^{-1}\), \(20\,\text{J s}^{-1}=20\,\text{W}\).
\( \textbf{Final answer:} \) The average power is \(20\,\text{W}\).
15. From the relation \(P_{\text{avg}}=\frac{W}{t}\), the dimensional formula of power is
ⓐ. \([ML^2T^{-2}]\)
ⓑ. \([MLT^{-3}]\)
ⓒ. \([M^2L^2T^{-3}]\)
ⓓ. \([ML^2T^{-3}]\)
Correct Answer: \([ML^2T^{-3}]\)
Explanation: \( \textbf{Starting relation:} \)
\[
P_{\text{avg}}=\frac{W}{t}
\]
Work has dimensional formula \([ML^2T^{-2}]\).
Time has dimensional formula \([T]\).
Dividing work by time gives
\[
[P]=\frac{[ML^2T^{-2}]}{[T]}
\]
Combining the powers of \(T\),
\[
[P]=[ML^2T^{-3}]
\]
This also matches the unit relation \(1\,\text{W}=1\,\text{J s}^{-1}\), where joule contributes \([ML^2T^{-2}]\) and per second adds one more \(T^{-1}\).
\( \textbf{Final answer:} \) The dimensional formula of power is \([ML^2T^{-3}]\).
16. A unit statement is written as \(1\,\text{W}=1\,\text{J s}^{-1}\). The meaning of this statement is that
ⓐ. one watt is one joule of energy stored
ⓑ. joule and watt name the same physical unit
ⓒ. one watt transfers one joule each second
ⓓ. one watt is one newton acting through one metre
Correct Answer: one watt transfers one joule each second
Explanation: The watt is the SI unit of power. Power measures how fast work is done or energy is transferred. The relation \(1\,\text{W}=1\,\text{J s}^{-1}\) says that a device has power \(1\,\text{W}\) when it transfers \(1\,\text{J}\) of energy in \(1\,\text{s}\). Joule measures the amount of work or energy, while watt measures the rate of that transfer. Confusing \( \text{J} \) with \( \text{W} \) removes the time factor that is central to power.
17. Mechanical work by a constant force is best described by the relation
ⓐ. \(W=Ft\)
ⓑ. \(W=Fv\)
ⓒ. \(W=Fs\sin\theta\)
ⓓ. \(W=Fs\cos\theta\)
Correct Answer: \(W=Fs\cos\theta\)
Explanation: Work done by a constant force depends on the force, the displacement, and the angle between them. The relation \(W=Fs\cos\theta\) includes only the component of force along displacement. If the force is exactly along displacement, \(\theta=0^\circ\) and \(\cos0^\circ=1\), so work becomes \(W=Fs\). If the force is perpendicular to displacement, \(\theta=90^\circ\) and the work becomes zero. Time may affect power, but it is not directly part of the constant-force work formula.
18. A force of \(10\,\text{N}\) acts on a body and the body is displaced by \(4\,\text{m}\). The force makes an angle of \(60^\circ\) with the displacement. What is the work done by the force?
ⓐ. \(20\,\text{J}\)
ⓑ. \(40\,\text{J}\)
ⓒ. \(10\,\text{J}\)
ⓓ. \(80\,\text{J}\)
Correct Answer: \(20\,\text{J}\)
Explanation: \( \textbf{Given data:} \) \(F=10\,\text{N}\), \(s=4\,\text{m}\), and \(\theta=60^\circ\).
\( \textbf{Required:} \) Work done by the force.
\( \textbf{Useful relation:} \)
\[
W=Fs\cos\theta
\]
This relation applies because the force is constant and acts at a fixed angle to the displacement.
\( \textbf{Angle factor:} \)
\[
\cos60^\circ=\frac{1}{2}
\]
\( \textbf{Substitution:} \)
\[
W=(10)(4)\left(\frac{1}{2}\right)
\]
\( \textbf{Calculation:} \)
\[
W=20\,\text{N m}
\]
Since \(1\,\text{N m}=1\,\text{J}\),
\[
W=20\,\text{J}
\]
\( \textbf{Final answer:} \) The work done is \(20\,\text{J}\).
19. A horizontal displacement is produced while a force acts obliquely upward on a block. For calculating work by this force, the useful part of the force is
ⓐ. only the vertical component
ⓑ. the full force magnitude without considering direction
ⓒ. the component perpendicular to the displacement
ⓓ. only the component along the horizontal displacement
Correct Answer: only the component along the horizontal displacement
Explanation: Work by a force depends on the component of that force along the displacement. If the displacement is horizontal, the horizontal component of the oblique force contributes to work. The vertical component does not produce work for purely horizontal displacement because it is perpendicular to displacement. Using the full force magnitude would overestimate the work unless the force itself is horizontal. The dot-product form \(W=\vec{F}\cdot\vec{s}\) automatically selects the along-displacement component.
20. The expression \(W=\vec{F}\cdot\vec{s}\) shows that work is a
ⓐ. vector quantity in the direction of \(\vec{F}\)
ⓑ. vector quantity in the direction of \(\vec{s}\)
ⓒ. scalar quantity from a scalar product
ⓓ. scalar quantity that is always positive
Correct Answer: scalar quantity from a scalar product
Explanation: The dot product of two vectors gives a scalar result. In \(W=\vec{F}\cdot\vec{s}\), both \(\vec{F}\) and \(\vec{s}\) are vectors, but their scalar product is work. Work can be positive, negative, or zero depending on the angle between force and displacement. A positive or negative sign in work does not make it a vector; it only shows the nature of energy transfer. Direction belongs to \(\vec{F}\) and \(\vec{s}\), while work itself has no direction in space.
