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Difficulty: MediumScalars and Vectors

Match each physical quantity or scenario on the left with its correct scalar or vector classification and physical property on the right.

  • Displacement of a particle moving in a complete circular track of radius rrVector quantity that depends strictly on initial and final positions, evaluating to zero for any closed path.
  • Work done on a wooden box pushed along a horizontal friction-free surfaceScalar quantity defined as the dot product of force and displacement vectors, having magnitude but no directional orientation.
  • Impulse imparted by a vertical wall to a bouncing rubber ballVector quantity equal to the time rate change of momentum integrated over time, possessing both magnitude and spatial direction.
  • Hydrostatic pressure exerted by a fluid at a depth hhScalar quantity defined as normal force per unit surface area, acting with equal magnitude in all directions at a given depth.

Answer

The correct pairings are: (1) Displacement on a closed track matches Vector quantity depending on initial and final positions (evaluating to zero); (2) Work done matches Scalar quantity defined as the dot product of force and displacement; (3) Impulse matches Vector quantity equal to change in momentum with spatial direction; (4) Hydrostatic pressure matches Scalar quantity defined as normal force per unit area acting equally in all directions.
Each physical quantity is categorized accurately based on vector/scalar definition: Displacement is a vector that evaluates to zero over a closed loop. Work done is a scalar derived from the vector dot product. Impulse is a vector defined by momentum change direction. Hydrostatic pressure is a scalar acting equally in all directions at a fluid depth.

Step-by-Step Solution

1
Analyze item 1: Displacement of a particle moving in a complete circular track of radius rr
Displacement is a vector pointing from start to end position. Since the path returns to the start, the magnitude is 0 m0\text{ m}.
Vectors require direction and position change; returning to origin yields zero vector displacement.
2
Analyze item 2: Work done on a wooden box pushed horizontally
Work is calculated using W=F⃗⋅s⃗=Fscos⁡θW = \vec{F} \cdot \vec{s} = F s \cos\theta, which yields a scalar value measured in Joules.
The dot product of two vectors produces a scalar quantity.
3
Analyze item 3: Impulse imparted by a vertical wall to a bouncing rubber ball
Impulse is defined as J⃗=F⃗avgΔt=Δp⃗\vec{J} = \vec{F}_{avg} \Delta t = \Delta \vec{p}. It is a vector pointing away from the wall.
Impulse has the direction of the applied average force or change in momentum vector.
4
Analyze item 4: Hydrostatic pressure exerted by a fluid at depth hh
Pressure is calculated as P=ρghP = \rho g h. It acts omnidirectionally at any point in fluid statics.
Because pressure at a point has no preferred direction, it is classified as a scalar physical quantity.

Key Concept

Classification of Physical Quantities into Scalars and Vectors based on Directional Properties
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Topics

Scalars and Vectors

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