JEE Advanced2018PhysicsLaws of MotionActual
A particle of mass m is initially at rest at the origin. It is subjected to a force and starts moving along the x - axis. Its kinetic energy changes with time as d K / d t = γ t , where γ is a positive constant of appropriate dimensions. Which of the following statements is (are) true?
Options
- AThe force applied on the particle is constant
- BThe speed of the particle is proportional to time
- CThe distance of the particle from the origin increases linearly with time
- DSince force is constant, it is conservative.
Correct answer
A. The force applied on the particle is constant
Step-by-step solution
Given the change in kinetic energy d k d t = γ t . Kinetic energy is expressed as k = 1 2 m v 2 . ∴       d k d t = m v d v d t = γ t Integrating the above relation, m ∫ 0 v v d v = γ ∫ 0 t t d t m v 2 2 = γ t 2 2 v = γ m t ; υ ∝ t ... (i) a = d v d t = γ m = c o n s t a n t Since F = m a ∴     F = m γ m = γ m = c o n s t a n t