OnlineCBT
Physics · WORK, ENERGY AND POWER
हिन्दीGiven below are statements regarding conservative forces and potential energy: (A) A force \( F(x) \) is conservative if it can be derived from a scalar potential \( V(x) \) via \( F(x) = -dV/dx \). (B) The work done by a conservative force in a closed loop is strictly non-zero. (C) The dimensions of the spring constant \( k \) are \( [\text{M}\text{T}^{-2}] \). (D) For an ideal spring obeying Hooke's law, the work done by the spring force when it returns from extension \( x_m \) back to equilibrium is positive. Choose the correct answer from the options given below:
Correct answer · Option 3
(A), (C) and (D) only
Explanation
Work done by a conservative force in any closed path is zero, so (B) is incorrect. (A) is correct (\( F = -dV/dx \)). (C) is correct (\( k = F/x \implies [\text{MT}^{-2}] \)). (D) is correct: from \( x_m \) to 0, \( W_s = \frac{1}{2}k x_m^2 > 0 \). Hence, (A), (C), and (D) are correct.
