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A force f= -k(yi-xj) (where k is constant) act on a particle moving in the xy plane. Starting from the origin the particle is taken along y-axis to the point (0,a). The work done by agent applying the force f on the particle is Opt 1 K^2(x^2 y^2) opt 2 zero Opt 3 Ky. Opt 4 kx?
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A force f= -k(yi-xj) (where k is constant) act on a particle moving in...
Answer:
Introduction:
In this problem, we have to find the work done by the agent applying the force f on the particle moving in the xy-plane.
Given:
Force f= -k(yi-xj) (where k is constant)
Calculation:
Let's take the particle from the origin to the point (0,a) along the y-axis.
The work done by the agent applying the force f on the particle is given by the formula:
W = ∫ (F . ds)
Where F is the force applied, ds is the displacement of the particle.
Let's calculate the work done in this case.
The displacement of the particle is ds = dy j, where j is the unit vector along the y-axis.
The force applied by the agent is F = -k(yi-xj), where i and j are the unit vectors along the x and y-axis respectively.
So, the dot product of F and ds is given by:
F . ds = (-k(yi-xj)) . (dy j) = -k(y dy)
Therefore, the work done by the agent is:
W = ∫ (-k(y dy)) = -k/2 (a^2 - 0^2) = -k/2 a^2
Hence, the correct option is Opt 1: K^2(x^2 y^2).
Conclusion:
The work done by the agent applying the force f on the particle is -k/2 a^2.
Introduction:
In this problem, we have to find the work done by the agent applying the force f on the particle moving in the xy-plane.
Given:
Force f= -k(yi-xj) (where k is constant)
Calculation:
Let's take the particle from the origin to the point (0,a) along the y-axis.
The work done by the agent applying the force f on the particle is given by the formula:
W = ∫ (F . ds)
Where F is the force applied, ds is the displacement of the particle.
Let's calculate the work done in this case.
The displacement of the particle is ds = dy j, where j is the unit vector along the y-axis.
The force applied by the agent is F = -k(yi-xj), where i and j are the unit vectors along the x and y-axis respectively.
So, the dot product of F and ds is given by:
F . ds = (-k(yi-xj)) . (dy j) = -k(y dy)
Therefore, the work done by the agent is:
W = ∫ (-k(y dy)) = -k/2 (a^2 - 0^2) = -k/2 a^2
Hence, the correct option is Opt 1: K^2(x^2 y^2).
Conclusion:
The work done by the agent applying the force f on the particle is -k/2 a^2.
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A force f= -k(yi-xj) (where k is constant) act on a particle moving in the xy plane. Starting from the origin the particle is taken along y-axis to the point (0,a). The work done by agent applying the force f on the particle is Opt 1 K^2(x^2 y^2) opt 2 zero Opt 3 Ky. Opt 4 kx? for NEET 2026 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A force f= -k(yi-xj) (where k is constant) act on a particle moving in the xy plane. Starting from the origin the particle is taken along y-axis to the point (0,a). The work done by agent applying the force f on the particle is Opt 1 K^2(x^2 y^2) opt 2 zero Opt 3 Ky. Opt 4 kx? covers all topics & solutions for NEET 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A force f= -k(yi-xj) (where k is constant) act on a particle moving in the xy plane. Starting from the origin the particle is taken along y-axis to the point (0,a). The work done by agent applying the force f on the particle is Opt 1 K^2(x^2 y^2) opt 2 zero Opt 3 Ky. Opt 4 kx?.
A force f= -k(yi-xj) (where k is constant) act on a particle moving in the xy plane. Starting from the origin the particle is taken along y-axis to the point (0,a). The work done by agent applying the force f on the particle is Opt 1 K^2(x^2 y^2) opt 2 zero Opt 3 Ky. Opt 4 kx? for NEET 2026 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A force f= -k(yi-xj) (where k is constant) act on a particle moving in the xy plane. Starting from the origin the particle is taken along y-axis to the point (0,a). The work done by agent applying the force f on the particle is Opt 1 K^2(x^2 y^2) opt 2 zero Opt 3 Ky. Opt 4 kx? covers all topics & solutions for NEET 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A force f= -k(yi-xj) (where k is constant) act on a particle moving in the xy plane. Starting from the origin the particle is taken along y-axis to the point (0,a). The work done by agent applying the force f on the particle is Opt 1 K^2(x^2 y^2) opt 2 zero Opt 3 Ky. Opt 4 kx?.
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