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3-2.Motion in Plane
hard
The dumbell is placed on a frictionless horizontal table. Sphere $A$ is attached to a frictionless pivot so that $B$ can be made to rotate about $A$ with constant angular velocity. If $B$ makes one revolution in period $P$, the tension in the rod is
A$\frac{{4{\pi ^2}Md}}{{{P^2}}}$
B$\frac{{8{\pi ^2}Md}}{{{P^2}}}$
C$\frac{{4{\pi ^2}Md}}{P}$
D$\frac{{2Md}}{P}$
Solution
$T_0=m R w_0^2$
$l^{\prime}=2 l$
$w^{\prime}=2 w^0$
$T^{\prime}=2 m l \times 4 w_0^2$
$T^{\prime}=8 T_0$
$T_0=\frac{\pi^2 Md }{p^2}$
$\therefore T^{\prime}=\frac{8 \pi^2 Md }{ p ^2}$
$l^{\prime}=2 l$
$w^{\prime}=2 w^0$
$T^{\prime}=2 m l \times 4 w_0^2$
$T^{\prime}=8 T_0$
$T_0=\frac{\pi^2 Md }{p^2}$
$\therefore T^{\prime}=\frac{8 \pi^2 Md }{ p ^2}$
Standard 11
Physics
