NEETPhysicsWork, Power and Energy
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): When a particle of mass m is released from rest at x=0 in a region where the one-dimensional force acting on it is given by F(x) = F₀ - kx (where F₀ and k are positive constants), its maximum kinetic energy during the subsequent motion is F₀^2 2k . Reason (R): The kinetic energy of the particle is
Options
- ABoth (A) and (R) are true and (R) is the correct explanation of (A)
- BBoth (A) and (R) are true but (R) is not the correct explanation of (A)
- C(A) is true but (R) is false
- D(A) is false but (R) is true
Correct answer
C. (A) is true but (R) is false
Step-by-step solution
The kinetic energy of the particle is maximum when its velocity is maximum, which occurs when its acceleration (and thus the net force) becomes zero. Setting F(x) = 0 : F₀ - kx = 0 x = F₀ k The maximum kinetic energy is equal to the work done by the force up to this position. Using the work-energy theorem: W = ₀^ F₀ k (F₀ - kx) dx W = [ F₀ x - k x^2 2 ]₀^ F₀ k W = F₀ ( F₀ k ) - k 2 ( F₀ k )^2 W = F₀^2 k - F₀^2 2k = F₀^2 2k Thus, the maximum kinetic energy is F₀^2 2k , making the Assertion (A) true. At the position