A particle of mass m is acted upon by a force F given by the empirical law F = R t ^ 2 v(t) . If this law is to be tested experimentally by observing the motion starting from rest, the best way is to plot

Correct answer: A. log v(t)against(1)/(t) F = R t ^ 2 v(t) ⇒ m(dv)/(dt) = R t ^ 2 v(t) ∫ (dv)/(v) = ∫ Rdt m t ^ 2 ln v = - (R)/(mt) ∴ v ∝ (1)/(t)

JEE Main 201610 AprilOnline

JEE Main 2016 · 10 April · Online · Physics · Laws of Motion

A particle of mass m is acted upon by a force F given by the...

A particle of mass

m

is acted upon by a force

F

given by the empirical law

F = \dfrac{R}{{t}^{2}}v\left(t\right) .

If this law is to be tested experimentally by observing the motion starting from rest, the best way is to plot

A. $log v\left(t\right)against\dfrac{1}{t}$

F = \dfrac{R}{{t}^{2}}v\left(t\right) ⇒ m\dfrac{dv}{dt} = \dfrac{R}{{t}^{2}}v\left(t\right)

∫ \dfrac{dv}{v} = ∫ \dfrac{Rdt}{m{t}^{2}}

v = - \dfrac{R}{mt}

∴ \ln v ∝ \dfrac{1}{t}