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Work and Energy — Physics STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 SciencePhysicsWork and Energy3 Marks
Question
A simple pendulum consists of a 50cm long string connected to a 100g ball. The ball is pulled aside so that the string makes an angle of 37° with the vertical and is then released. Find the tension in the string when the bob is at its lowest position.
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Answer

From the figure, $\cos\theta=\frac{\text{AC}}{\text{AB}}$
$\Rightarrow\text{AC}=\text{AB}\cos\theta$
$\Rightarrow(0.5)\times(0.8)=0.4$
So, CD = (0.5) - (0.4) = (0.1)m Energy at D = energy at B$\frac{1}{2}\text{mv}^2=\text{mg}(\text{CD})$
$\text{v}^2=2\times10\times(0.1)=2$
So, the tension is given by,$\text{T}=\frac{\text{mv}^2}{\text{r}}+\text{mg}$
$\Rightarrow(0.1)\Big(\frac{2}{0.5}+10\Big)=1.4\text{N}$

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