the work done in moving an object from origin to a point whose position vector is r =3i +2j -5k by a force F= 2i -j -k is
Correct answer: B. 9 units
- A. 1 unit
- B. 9 units
- C. 13 units
- D. 60 units
Explanation
The work done by a force is the dot product of the force and the displacement.1. Calculate the displacement vector:The displacement vector from the origin to the point specified by the position vector is simply the position vector itself:displacement = r = 3i + 2j - 5k2. Calculate the dot product:The dot product of the force vector (F) and the displacement vector (r) is:work = F • r = (2i - j - k) • (3i + 2j - 5k)work = (2 * 3) + (-1 * 2) + (-1 * -5)work = 6 - 2 + 5work = 9 unitsTherefore, the work done by the force is 9 units, which corresponds to answer choice b
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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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