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5.Work, Energy, Power and Collision
hard
A particle is whirled in a vertical circle of radius $1.0\ m$ using a string with one end fixed. If the ratio of maximum and minimum tension in the string is $\frac{5}{3}$, the minimum velocity of the particle during circular motion is ......... $ms^{-1}$
A
$\sqrt {10} $
B
$\sqrt {50}$
C
$10$
D
$10\sqrt 5 $
Solution
$\mathrm{T}_{\mathrm{max}}-\mathrm{mg}=\frac{\mathrm{mv}_{\mathrm{max}}^{2}}{\mathrm{R}}$
$\mathrm{mg}+\mathrm{T}_{\mathrm{min}}=\frac{\mathrm{mv}_{\mathrm{min}}^{2}}{\mathrm{R}}$
$\frac{T_{\max }}{T_{\min }}=\frac{\frac{v_{\max }^{2}}{R}+g}{\frac{v_{\min }^{2}}{R}-g}$
$\Rightarrow \mathrm{v}_{\mathrm{m} \mathrm{in}}=10 \mathrm{m} / \mathrm{s}$
Standard 11
Physics
