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3-2.Motion in Plane
easy
A ball of mass $0.1\, Kg$. is whirled in a horizontal circle of radius $1\, m$. by means of a string at an initial speed of $10\, R.P.M.$ Keeping the radius constant, the tension in the string is reduced to one quarter of its initial value. The new speed is ....... $r.p.m.$
A$5$
B$10$
C$20$
D$14$
Solution
(a) $T = m{\omega ^2}r$ $⇒$ $\omega \propto \sqrt T $
$\therefore \frac{{{\omega _2}}}{{{\omega _1}}} = \sqrt {\frac{1}{4}} $ $\Rightarrow {\omega _2} = \frac{{{\omega _1}}}{2} = 5\,rpm$
$\therefore \frac{{{\omega _2}}}{{{\omega _1}}} = \sqrt {\frac{1}{4}} $ $\Rightarrow {\omega _2} = \frac{{{\omega _1}}}{2} = 5\,rpm$
Standard 11
Physics
