Laws of Motion

JEE Main level, single correct, medium

48 of 210

Question 48 of 210

A particle of mass mm is acted upon by a force FF given by the empirical law F=Rt2v(t).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

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Answer: (A) log⁡⁡v(t)against1t\log ⁡v\left(t\right)against\dfrac{1}{t}

F=Rt2v(t)⇒mdvdt=Rt2v(t)F=\dfrac{R}{{t}^{2}}v\left(t\right)\Rightarrow m\dfrac{dv}{dt}=\dfrac{R}{{t}^{2}}v\left(t\right)

∫dvv=∫Rdtmt2\int \dfrac{dv}{v}=\int \dfrac{Rdt}{m{t}^{2}}

ln v=−Rmtv=-\dfrac{R}{mt}

∴ln⁡v∝1t∴\ln v\propto \dfrac{1}{t}

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