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3-2.Motion in Plane
hard
$A \,10\, kg$ ball attached to the end of a rigid massless rod of length $1\, m$ rotates at constant speed in a horizontal circle of radius $0.5\, m$ and period $1.57 \, sec$ as in fig. The force exerted by rod on the ball is ........ $N$.
A$1.28$
B$128$
C$10$
D$12.8$
Solution
Let, $\omega$ is angular velocity.
Forces on the ball: $m g \downarrow, m \omega^{2} r \leftarrow,$ Normalreaction, $N_{1}$ perpendicular to length of the rod, Hinge reaction, $N_{2}$ in the direction of length of the rod.
$\omega=\frac{2 \pi}{T} N_{1}=m g \cos \left(\frac{\pi}{3}\right)+m \omega^{2} r \sin \left(\frac{\pi}{3}\right) N_{2}=m g \sin \left(\frac{\pi}{3}\right)-m \omega^{2} \cos \left(\frac{\pi}{3}\right)$
Net force exerted by rod on the ball $N=\sqrt {{N_1}^{2} + {N_2}^{2}}$
Solving this, we get $N=128 N$
Forces on the ball: $m g \downarrow, m \omega^{2} r \leftarrow,$ Normalreaction, $N_{1}$ perpendicular to length of the rod, Hinge reaction, $N_{2}$ in the direction of length of the rod.
$\omega=\frac{2 \pi}{T} N_{1}=m g \cos \left(\frac{\pi}{3}\right)+m \omega^{2} r \sin \left(\frac{\pi}{3}\right) N_{2}=m g \sin \left(\frac{\pi}{3}\right)-m \omega^{2} \cos \left(\frac{\pi}{3}\right)$
Net force exerted by rod on the ball $N=\sqrt {{N_1}^{2} + {N_2}^{2}}$
Solving this, we get $N=128 N$
Standard 11
Physics
