CBSE-XI-Physics
05: Newton's Laws of Motion
- #21A force
F→=v→×A→is exerted on a particle in addition to the force of gravity, where
v→is the velocity of the particle and
A→is a constant vector in the horizontal direction. With what minimum speed, a particle of mass m be projected so that it continues to move without being defelected and with a constant velocity?Ans : For the particle to move without being deflected and with constant velocity, the net force on the particle should be zero.
`` \stackrel{\to }{F}+m\stackrel{\to }{g}=0``
`` \Rightarrow \left(\stackrel{\to }{v}\times \stackrel{\to }{A}\right)+\stackrel{\to }{mg}=0``
`` \Rightarrow \left(\stackrel{\to }{v}\times \stackrel{\to }{A}\right)=-\stackrel{\to }{mg}``
`` \left|vA\,\mathrm{\,sin \,}\theta \right|=\left|mg\right|``
`` \therefore v=\frac{mg}{A\,\mathrm{\,sin \,}\theta }``
v will be minimum when sinθ = 1.
⇒ θ = 90°
`` \therefore {v}_{min}=\frac{mg}{A}``
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