Question

A particle is taken from point A to point B under the influence of a force field. Now it is taken back from B to A and it is observed that the work done in taking the particle from A to B is not equal to the work done in taking it from B to A. If ${W_ {nc}}$ and ${W_c}$ are work done by non-conservative and conservative forces present in the system, respectively, $\Delta U$ is the change in potential energy and $\Delta K$ is the change in kinetic energy, then
This question has multiple correct options
A. ${W_ {nc}} - \Delta U = \Delta K$
B. ${W_c} = - \Delta U$
C. ${W_ {nc}} + {W_c} = \Delta K$
D. ${W_ {nc}} - \Delta U = - \Delta K$

Answer 1

Here, we have to given that a particle is taken from point A to point B under the influence of a force field and also back from B to A and it is observed that the work done in taking the particle from A to B is not equal to the work done in taking it from B to A. We have to find $\Delta U$ and $\Delta K$.

Complete step by step solution:
In the given question, firstly we have defined conservative force and non conservative force because, work done present in the system. A conservative force is a force with the property that the total work in moving a particle between two points is independent of the taken path. That is, the total work done by a conservative force is zero. And non conservative force is path dependent.
Thus, the work done by all forces is the change in kinetic energy,
${W_ {nc}} + {W_c} = \Delta K$

Also, only the conservative force can change the potential energy of the system.
Therefore, ${W_c} = - \Delta U$

On putting the value of ${W_c}$ in the above equation, we get
${W_ {nc}} - \Delta U = \Delta K$

Therefore, option A, B and C are correct answer.

Note: Here, we have to clear the concept of conservative and non conservative force. Be careful during the calculation that the work done dependent or independent of the taken path and the total work done is equal to the sum of kinetic energy.