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  4. A stone of mass 1 kg is tied with a string and it is whirled in a vertical circle of radius 1 m. If tension at the highest point is 14 N, then velocity at lowest point will be

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Q. A stone of mass $1\, kg$ is tied with a string and it is whirled in a vertical circle of radius $1\, m$. If tension at the highest point is $14\, N$, then velocity at lowest point will be

Work, Energy and Power

Solution:

$T+m g=\frac{m v^{2}}{R}$ (at the highest point)
$14=\frac{1\left(v^{2}\right)}{R(1)}+10$
$v^{2}=4 \quad \Rightarrow v=2\, m / s$
Using mechanical energy conservation.
$\frac{1}{2}(1) u^{2}=\frac{1}{2}(1)\left(2^{2}\right)+1(10)(2)$
$u^{2}=64$
$\Rightarrow u=8\, m / s$