Question

A pendulum bob of mass m is suspended at rest. A constant horizontal force f=mg/2 starts acting on it. The maximum angular deflection of the string is

Answer 1

the answer is 37

Explanation:

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Answer 2

Answer:

The maximum angular deflection of the string is $\theta=53^{\circ} \text { }$.

Explanation:

In gunnery, the angle between the line of sight to the target and the line of sight to the aiming point for a deflection shot.

Let angular deflection be $\theta$ when velocity is $v$,

then by work energy theorem $W=\triangle K E$

$\frac{1}{2} m v^{2}=-m g h+F I \sin \theta$

$\frac{1}{2} m v^{2}=-m g(\cos \theta)+FI\sin \theta$

At maximum angular deflection, $v=0$

$\begin{aligned}&0=-m g \mid(1-\cos \theta)+\frac{m g}{2} \sin \theta \\&\Rightarrow 2-2 \cos \theta=\sin \theta \Rightarrow 4+4 \cos ^{2} \theta-8 \cos \theta=\sin ^{2} \theta=1-\cos ^{2} \theta \\&\Rightarrow 5 \cos ^{2} \theta-8 \cos \theta+3=0 \Rightarrow 5 \cos ^{2} \theta-5 \cos \theta-3 \cos \theta+3=0\end{aligned}$

$\begin{aligned}&\Rightarrow 5 \cos \theta(\cos \theta-1)-3(\cos \theta-1)=0 \\&\Rightarrow(5 \cos \theta-3)(\cos \theta-1)=0 \\&\Rightarrow \cos \theta=\frac{3}{5} \text { or } \cos \theta=1 \\&\Rightarrow \theta=53^{\circ} \text { or } \theta=0\end{aligned}$