COMEDK2022PhysicsWork, Power and Energy
A particle of mass m is moving in a horizontal circle of radius r under a centripetal force given by ( -K r^2 ) , where K is a constant. Then
Options
- Athe total energy of the particle is ( -K 2 r )
- Bthe kinetic energy of the particle is ( K r )
- Cthe potential energy of the particle is ( K 2 r )
- Dthe kinetic energy of the particle is ( -K r )
Correct answer
A. the total energy of the particle is ( -K 2 r )
Step-by-step solution
The centripetal force acting on the particle is given by F = -K r^2 . The magnitude of the centripetal force is F_c = mv^2 r = K r^2 . From this, the kinetic energy K.E. is calculated as K.E. = 1 2 mv^2 = 1 2 ( K r ) = K 2r . The potential energy U is defined by F = - dU dr . Integrating the force F = - K r^2 with respect to r , we get U = K r^2 dr = - K r . The total energy E is the sum of kinetic energy and potential energy: E = K.E. + U = K 2r - K r = - K 2r . Comparing this with the given options, the total ene