`S_(1):` If the internal forces within a system are conservative, then the work done by the external forces on the system is equal to the change in mechanical energy of the system.
`S_(2):` The potential energy of a particle moving along `x-` axis in a conservative force field is `U=2x^(2)-5x+1` is `S.I.` units. No other forces are acting on it. It has a stable equalibrium position at one point on `x-` axis.
`S_(3) :`Internal forces can perform net work on a rigid body.
`S_(4) :` Internal forces can perform net work on a non`-` rigid body.

Options

A. `T T F T`
B. `T F F T`
C. `F F T T `
D. `F T F T `

Answer

A

Explanation

`S_(1):` The statement is true from Work Energy Theorem
`S_(2): F=-(dU)/(dx)=-4x+5 :. SHM`
`S_(3) & S_(4):` A rigid body by definition cannot be expanded or compressed, thus it cannot store mechanical potential energy. Hence internal forces can do no work on rigid body, but can do work on non`-` rigid body. Hence `S_(3)` is false and `S_(4)` is true.