A particle of mass M originally at rest is subjected to a force whose direction is constant but magnitude varies with time according to the relation
A particle of mass M originally at rest is subjected to a force whose direction is constant but magnitude varies with time according to the relation
$\mathrm{F}=\mathrm{F}_{0}\left[1-\left(\frac{\mathrm{t}-\mathrm{T}}{\mathrm{T}}\right)^{2}\right]$
Where $\mathrm{F}_{0}$ and $\mathrm{T}$ are constants. The force acts only for the time interval $2 \mathrm{~T}$. The velocity $\mathrm{v}$ of the particle after time $2 \mathrm{~T}$ is :
Correct Option: , 3
$\mathrm{t}=0, \mathrm{u}=0$
$\mathrm{a}=\frac{\mathrm{F}_{\mathrm{o}}}{\mathrm{M}}-\frac{\mathrm{F}_{\mathrm{o}}}{\mathrm{MT}^{2}}(\mathrm{t}-\mathrm{T})^{2}=\frac{\mathrm{dv}}{\mathrm{dt}}$
$\int_{0}^{\mathrm{v}} \mathrm{dv}=\int_{\mathrm{t}=0}^{2 \mathrm{~T}}\left(\frac{\mathrm{F}_{\mathrm{o}}}{\mathrm{M}}-\frac{\mathrm{F}_{\mathrm{o}}}{\mathrm{MT}^{2}}(\mathrm{t}-\mathrm{T})^{2}\right) \mathrm{dt}$
$\mathrm{V}=\left[\frac{\mathrm{F}_{\mathrm{o}}}{\mathrm{M}} \mathrm{t}\right]_{0}^{2 \mathrm{~T}}-\frac{\mathrm{F}_{\mathrm{o}}}{\mathrm{MT}^{2}}\left[\frac{\mathrm{t}^{3}}{3}-\mathrm{t}^{2} \mathrm{~T}+\mathrm{T}^{2} \mathrm{t}\right]_{0}^{2 \mathrm{~T}}$
$V=\frac{4 F_{0} T}{3 M}$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.