The velocity ( v ) of a particle (under a force F ) depends on its distance ( x ) from the origin (with x 0 ) v ∝ x 1 . Find how the magnitude of the force ( F ) on the particle depends on x ?

Question

The velocity ( v ) of a particle (under a force F ) depends on its distance ( x ) from the origin (with x > 0 ) v ∝ x ​ 1 ​ . Find how the magnitude of the force ( F ) on the particle depends on x ?

TestHub · Accepted Answer

According to the question. v ∝ x ​ 1 ​ or v = x ​ k ​ d t d v ​ = d t d ​ ⋅ x ​ K ​ = k ⋅ 2 − 1 ​ ⋅ x − 2 1 ​ − 1 ⋅ d t d x ​ a = − 2 k ​ ⋅ x − 2 3 ​ ⋅ x ​ k ​ [ ∵ d t d x ​ = v and v = x ​ k ​ from Eq ( i ) ] = 2 − k 2 ​ ⋅ x 2 1 ​ = m 2 k 2 ​ ⋅ x 2 1 ​ (magnitue F = 2 k 2 ​ ⋅ x 2 m ​ ∴ F x x 2 1 ​

Physics - NLM Question with Solution | TestHub

Options:

Doubts & Discussion