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Olympiad workbook
Exam
Olympiad workbook
Subject
NSEP
Chapter
Work, Power and Energy

Olympiad workbook · NSEP · Work, Power and Energy

Motion of a particle in a plane is described by the non-orthogonal...

Motion of a particle in a plane is described by the non-orthogonal set of coordinates (p,q)(p, q) with unit vectors ( p^,q^\hat{p}, \hat{q} ) inclined at an angle θ\theta as shown in the diagram. If the mass of the particle is mm, its kinetic energy is given by (x˙=dxdt)\left(\dot{x}=\frac{d x}{d t}\right) Motion of a particle in a plane is described by the non-orthogonal set of coordinates (p, q) with unit vectors ( p , q

Options

  1. A12m\frac{1}{2} m\left(\dot{p}^2+\dot{q}^2+\dot{p} \dot{q} \cos \theta\right)
  2. B12m\frac{1}{2} m\left(\dot{p}^2+\dot{q}^2-\dot{p} \dot{q}(1-\sin \theta)\right)
  3. C12m\frac{1}{2} m\left(\dot{p}^2+\dot{q}^2+2 \dot{p} \dot{q} \cos \theta\right)
  4. D12m\frac{1}{2} m\left(\dot{p}^2+\dot{q}^2+\dot{p} \dot{q} \cot \theta\right)

Correct answer

C. 12m\frac{1}{2} m\left(\dot{p}^2+\dot{q}^2+2 \dot{p} \dot{q} \cos \theta\right)

Step-by-step solution

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