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Question
The bob of a simple pendulum of length 1 m has mass 100 g and a speed of 1.4 m/s at the lowest point in its path. Find the tension in the string at this instant.
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Solution
Given:
Mass of the bob = m = 100 gm = 0.1 kg
Length of the string = r = 1 m
Speed of bob at the lowest point in its path = 1.4 m/s
Let T be the tension in the string.
From the free body diagram,
we get :
\[\text{T = mg }+ \frac{\text{mv}^2}{\text{r}}\]
\[ = \left( \frac{1}{10} \right) \times 9 . 8 + \frac{(1 . 4 )^2}{10}\]
\[ = 0 . 98 + 0 . 196\]
\[ = 1 . 176 \approx 1 . 2 \text{N}\]
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