Question

A $10kg$ ball attached at the end of a rigid massless rod of length $1m$ rotates at constant speed in a horizontal circle of radius $0.5m$ and period of $1.58s$, as shown in the figure. The force exerted by the rod on the ball is $(g=10m{s}^{-2})$

• A. $158N$
• B. $128N$
• C. $110N$
• D. $98N$

Answer 1

Answer: (B)

$128N$

Force acting on ball:

1. Downward force by weight of ball $mg$

2. Force by road in upward direction $F_1$

3. Centripital force in horizontal direction $F_c$

Balancing force in vertical direction

$F_1=mg=100N$

velocity of ball $v=\frac{2\pi r}{T}=\frac{2\pi 0.5}{1.58}=2m/s$

and $F_c=\frac{m{v}^2}{r}=\frac{10\times 2^2}{0.5}=80N$

$F_{net}=\sqrt{F_1^2+F_c^2}$

$F_{net}=\sqrt{{100}^2+{80}^2}=128N$