Question

Length of a simple pendulum is $2m$ and mass of its bob is $0.2kg$. If the tension in the string exceeds $4N$, it will break. If the bob is whirled in horizontal plane, the maximum angle the string can make with vertical during rotation is

• A. ${30}^o$
• B. ${45}^o$
• C. ${60}^o$
• D. ${90}^o$

Answer 1

The correct option is C ${60}^o$

The force on bob are Tension T in the string along the string from the bob, and the weight mg of the bob vertically downward. The tension makes an angle of $\varphi$ with the vertical. Let the bob move in a horizontal circle with a uniform velocity.

$T\cos \varphi =mg$ and $T\sin \varphi =\frac{m{v}^2}{R}=centripetalforce$

$\cos \varphi =\frac{mg}{T}=\frac{0.2kg\times 10m/s^2}{4N}=0.5$

Maximum angle $=\varphi =60°$