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The velocity (v) of a particle (under a ...

The velocity (v) of a particle (under a force F) depends on its distance (x) from the origin (with `x gt0`) `v prop(1)/(sqrt(x))`. Find how the magnitude of the force (F) on the particle depends on x.

A

`F prop 1/(x^(3//2))`

B

`F prop 1/x`

C

`F prop 1/x^(2)`

D

`F prop x`

Text Solution

Verified by Experts

The correct Answer is:
C
the velocity of a particle under force from the origin, `v prop 1/sqrt(x)`
Differentiating both sides, with respect to time t, we get
`(dv)/(dt) = 1/(2x^(3//2)) (dx)/(dt)` or `(dv)/(dt) = 1/(2x^(3//2)_). 1/(x^(1//2))`
`(dv)/(dt) = 1/(2x^(2))`
Multiplying both sides by mass m, we get
`m xx (dv)/(dt) = m xx 1/(2x^(2))` or `F prop 1/x^(2)`
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