Force acting on a particle moving in a straight line varies with the velocity of the particle as F=K/V. Here K is constant. The work done by this force in time t is:
Correct answer: C. Work done is directly related to the integral of K/V over time
- A. Work done is proportional to velocity squared
- B. Work done is equal to the product of force and time
- C. Work done is directly related to the integral of K/V over time
- D. Work done is constant regardless of the particle's velocity
Explanation
The correct answer is Option C. The force acting on the particle is given by F = K/V, indicating that the force decreases as velocity increases. To find the work done over time t, we need to integrate the force with respect to distance, which involves taking into account how the velocity changes as a function of time. The work done can be expressed as W = ∫ F dx, and since F depends on velocity, we substitute F with K/V and integrate accordingly.Option A is incorrect because it assumes a direct relationship with velocity squared, which is not supported by the given relationship. Option B is simplistic and overlooks the velocity dependency of the force. Option D misrepresents the nature of the force, as the work done cannot be constant if the force is changing with velocity.
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About Work and Energy
Work transfers energy when a force causes displacement, while kinetic energy, gravitational potential energy and power describe motion, position and the rate of energy transfer. The work-energy theorem links net work with change in kinetic energy, and efficiency accounts for energy losses rather than treating them as energy destruction.
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