Question

A stone of mass 0.5 kg is attached to a string of length 2 m and is whirled in a horizontal circle. If the string can with stand a tension of 9N, the maximum velocity with which the stone can be whirled is ?

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Answer 1

$\: {\Large{\rm{Given }}}\: :\: \\ \\ \: \: \: \: \: \bullet \rm \: Mass \: (M) \: = \: 0.5 \: kg \\\\ \: \: \: \: \: \bullet \rm \:Radius \: (R) \: = \: 2 \: m \\\\ \: \: \: \: \: \bullet \rm \: Tension \: (T) \: = \: 9N \: \\ \\{\Large{\rm{To\:Find }}}\: :\\ \\ \: \: \: \: \: \bullet \rm \: Velocity_{(max)}\:which \: the \: stone \: can \: be \: whirled \\ \\ {\Large{\rm{Solution }}}\: : \\ \\ \rm Centrifugal \: force \: = \: tension \: in \: string\ \\ \\ \rm \: \frac{MV ^{2}}{r} = T \: \\ \\ \:\ \: \: \longrightarrow \: \rm \: V \: = \: \sqrt{ \frac{Tr}{M} } \: \\ \\ \: \: \: \: \longrightarrow \: \rm \: V \: = \: \sqrt{ \frac{9 \times 2}{0.5}} \: \\\\ \: \: \: \: \longrightarrow\:\rm \: V \: = \: 6 \: ms {}^{ - 1} \\ \\ \therefore \:\rm Maximum \: velocity \: of \: stone \: is \: 6 \: ms {}^{ - 1} \:$