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Concepts Of Physics MCQ Edition [Volume 1]
Exam
Concepts Of Physics MCQ Edition [Volume 1]
Subject
Physics
Chapter
Work and Energy

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Work and Energy

The kinetic energy of a particle increases continuously over time.

The kinetic energy of a particle increases continuously over time.

Options

  1. AThe magnitude of its linear momentum increases continuously.
  2. BThe resultant force on the particle must always form an angle of less than 90^{}^{{}^{\circ}} with the velocity.
  3. CIts height above ground level must continuously decrease.
  4. DThe resultant force on the particle must be parallel to its velocity at all instants.

Correct answer

B. The resultant force on the particle must always form an angle of less than 90^{}^{{}^{\circ}} with the velocity.

Step-by-step solution

The kinetic energy of a particle is given by K=p22mK = \dfrac{p^2}{2m}.

Since the kinetic energy increases continuously, the magnitude of its linear momentum pp must also increase continuously.

The rate of change of kinetic energy is equal to the power delivered by the net force, which is given by dKdt=F⃗⋅v⃗=Fvcos⁡θ\dfrac{dK}{dt} = \vec{F} \cdot \vec{v} = F v \cos \theta.

For the kinetic energy to increase continuously, dKdt>0\dfrac{dK}{dt} > 0, which implies cos⁡θ>0\cos \theta > 0.

Thus, the angle θ\theta between the resultant force and the velocity must always be less than 90^{}^{{}^{\circ}}.

The height of the particle does not necessarily decrease, as an upward force greater than gravity can increase both its height and kinetic energy.

The resultant force need not be strictly parallel to the velocity; it only requires a positive tangential component.
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