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For a particle moving on a curved path ...

For a particle moving on a curved path kinectic energy is given as k=AS where S is distance moved and A is constant quantity .Net force acting on particle is

A

less than A

B

equal to A

C

more than A

D

may be less than or equal to A

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To solve the problem, we need to determine the net force acting on a particle moving along a curved path, given that its kinetic energy is expressed as \( K = A \cdot S \), where \( S \) is the distance moved and \( A \) is a constant. ### Step-by-Step Solution: 1. **Express Kinetic Energy in Standard Form**: The kinetic energy \( K \) of a particle is given by the formula: \[ K = \frac{1}{2} mv^2 \] where \( m \) is the mass of the particle and \( v \) is its velocity. 2. **Set the Two Expressions for Kinetic Energy Equal**: According to the problem, we have: \[ K = A \cdot S \] Therefore, we can set the two expressions for kinetic energy equal to each other: \[ \frac{1}{2} mv^2 = A \cdot S \] 3. **Solve for \( mv^2 \)**: Rearranging the equation gives: \[ mv^2 = 2AS \] 4. **Relate Force to Acceleration**: For a particle moving in a curved path, the net force \( F \) acting on it can be expressed in terms of centripetal acceleration. The centripetal force required to keep the particle moving in a circle of radius \( r \) is given by: \[ F = \frac{mv^2}{r} \] 5. **Substitute \( mv^2 \) into the Force Equation**: Now, substituting \( mv^2 = 2AS \) into the force equation gives: \[ F = \frac{2AS}{r} \] 6. **Conclusion about the Net Force**: Since \( A \) is a constant and \( S \) is the distance moved (which is positive), the force can be expressed as: \[ F = \frac{2AS}{r} \] This indicates that the net force acting on the particle is proportional to \( S \) and is greater than \( A \) since \( F \) is a multiple of \( A \). ### Final Result: Thus, the net force acting on the particle is: \[ F = \frac{2AS}{r} \]
To solve the problem, we need to determine the net force acting on a particle moving along a curved path, given that its kinetic energy is expressed as \( K = A \cdot S \), where \( S \) is the distance moved and \( A \) is a constant. ### Step-by-Step Solution: 1. **Express Kinetic Energy in Standard Form**: The kinetic energy \( K \) of a particle is given by the formula: \[ K = \frac{1}{2} mv^2 ...
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