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A particle moves along y=sqrt(1-x^ (2)) ...

A particle moves along `y=sqrt(1-x^ (2))` between the points (0, -1) m and (0, 1) m under the influence of a force `vec(F)=(y^(2)hat(i)+x^(2)hat(j))N`. Then,

A

the particle is moving along a semi-ellipse

B

the particle is moving along a semicircle

C

work done on the particle by `vec(F)` by `3/4`J

D

work done on the particle by `vec(F)` is `4/3`J

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To solve the problem step by step, we will analyze the motion of the particle, identify the path it takes, and calculate the work done by the force acting on it. ### Step 1: Identify the Path of the Particle The equation of the path is given as \( y = \sqrt{1 - x^2} \). 1. **Square both sides** to eliminate the square root: \[ y^2 = 1 - x^2 \] Rearranging gives: \[ x^2 + y^2 = 1 \] This is the equation of a circle with radius 1 centered at the origin. 2. **Determine the points of interest**: The particle moves between the points \( (0, -1) \) and \( (0, 1) \). These points lie on the y-axis, indicating that the particle moves along the semicircle from the bottom point to the top point.
To solve the problem step by step, we will analyze the motion of the particle, identify the path it takes, and calculate the work done by the force acting on it. ### Step 1: Identify the Path of the Particle The equation of the path is given as \( y = \sqrt{1 - x^2} \). 1. **Square both sides** to eliminate the square root: \[ y^2 = 1 - x^2 ...
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