NIMCET 2020 Mathematics PYQ — Forces of magnitude , , units acts in directions , , respectively… | Mathem Solvex | Mathem Solvex
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NIMCET 2020 — Mathematics PYQ
NIMCET | Mathematics | 2020
Forces of magnitude 5, 3, 1 units acts in directions 6i^+2j^+3k^, 3i^−2j^+6k^, 2i^−3j^−6k^ respectively on a particle which is displaced from the point (2,−1,−3) to (5,−1,1). The total work done by the force is:
Choose the correct answer:
A.
21 units
B.
5 units
C.
33 units
(Correct Answer)
D.
105 units
Correct Answer:
33 units
Explanation
Concept: The work done W=(Fr)⋅(dx)
where Fr is the resultant force, and dx is the displacement
The unit vector in the direction of a P=∣P∣P
Calculation: The initial position of the particle (A) = 2i^−j^−3k^
The initial position of the particle (B) = 5i^−j^+k^
dx=B−A=(5i−j+k)−(2i−j−3k)=3i+4k First force F1 = magnitude of the 1st force × unit vector in the given direction <br>F1=5×∣6i+2j+3k∣6i+2j+3k=730i+10j+15k Second force F2 = magnitude of the 2nd force × unit vector in the given direction F2=3×∣3i−2j+6k∣3i−2j+6k=79i−6j+18k Third force F3 = magnitude of the 3rd force × unit vector in the given direction <br>F3=1×∣2i−3j−6k∣2i−3j−6k=72i−3j−6k Resultant Force Fr=F1+F2+F3 Fr=730i+10j+15k+79i−6j+18k+72i−3j−6k <br>Fr=741i+11j+27k The work done by the forces: W=(Fr)⋅(dx) <br>W=(741i+11j+27k)⋅(3i+4k) W=(7123i+108) <br>W=33 units
Explanation
Concept: The work done W=(Fr)⋅(dx)
where Fr is the resultant force, and dx is the displacement
The unit vector in the direction of a P=∣P∣P
Calculation: The initial position of the particle (A) = 2i^−j^−3k^
The initial position of the particle (B) = 5i^−j^+k^
dx=B−A=(5i−j+k)−(2i−j−3k)=3i+4k First force F1 = magnitude of the 1st force × unit vector in the given direction <br>F1=5×∣6i+2j+3k∣6i+2j+3k=730i+10j+15k Second force F2 = magnitude of the 2nd force × unit vector in the given direction F2=3×∣3i−2j+6k∣3i−2j+6k=79i−6j+18k Third force F3 = magnitude of the 3rd force × unit vector in the given direction <br>F3=1×∣2i−3j−6k∣2i−3j−6k=72i−3j−6k Resultant Force Fr=F1+F2+F3 Fr=730i+10j+15k+79i−6j+18k+72i−3j−6k <br>Fr=741i+11j+27k The work done by the forces: W=(Fr)⋅(dx) <br>W=(741i+11j+27k)⋅(3i+4k) W=(7123i+108) <br>W=33 units
