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3-2.Motion in Plane
medium
As shown in the figure, two strings of length $l$ each are attached with a vertical axis $AB$ of length $l$. Strings are $AC$ and $BC$. At point $C$ a point mass m is attached. Mass rotates about axis with angular velocity. Tensions in $AB$ and $BC$ are $T_1$ and $T_2$ respectively. Choose the $CORRECT$ alternative :-
A$T_1 = T_2$
Bstring $AC$ will remain taut only if $\omega \geq \sqrt{2g/l}$
Cstring $BC$ will remain taut for any value of $\omega$.
D$T_1 -T_2 = 2mg$
Solution
From the $F.B.D.$ of $m,$
$\mathrm{T}_{1}=\frac{\mathrm{m} \omega^{2} \ell}{2}+\mathrm{mg}, \mathrm{T}_{2}=\frac{\mathrm{m} \omega^{2} \ell}{2}-\mathrm{mg}$
$\mathrm{T}_{1}=\frac{\mathrm{m} \omega^{2} \ell}{2}+\mathrm{mg}, \mathrm{T}_{2}=\frac{\mathrm{m} \omega^{2} \ell}{2}-\mathrm{mg}$
Standard 11
Physics
