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NEET-XII-Physics

07: Circular Motion

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  • #6
    A particle is kept fixed on a turntable rotating uniformly. As seen from the ground the particle goes in a circle, its speed is 20 cm/s and acceleration is 20 cm/s2. The particle is now shifted to a new position to make the radius half of the original value. The new value of the speed and acceleration will be
    (a) 10 cm/s, 10 cm/s2
    (b) 10 cm/s, 80 cm/s2
    (c) 40 cm/s, 10 cm/s2
    (d) 40 cm/s, 40 cm/s2
    digAnsr:   a
    Ans : (a) 10 cm/s, 10 cm/s2
    It is given that the turntable is rotating with uniform angular velocity. Let the velocity be `` \omega ``.
    We have:
    `` v=r\omega ``
    `` \Rightarrow v\propto r(\,\mathrm{\,for \,}\,\mathrm{\,constant \,}\omega )``
    `` \frac{v}{v\text{ ' }}=\frac{r}{r\text{ ' }}``
    `` \Rightarrow v\text{ ' }=\frac{v}{2}=10\,\mathrm{\,cm \,}/\,\mathrm{\,s \,}``
    Similarly, we have:
    `` a\text{ ' }=\frac{a}{2}=10\,\mathrm{\,cm \,}/{\,\mathrm{\,s \,}}^{2}``