Answer
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Hint At the highest point, the tension in the string and weight of the body together provides the necessary centripetal force required for rotation of the body in a circular path. Hence, $\text{T +}\,\text{mg = }\dfrac{\text{m}{{\text{v}}^{\text{2}}}}{\text{r}}$ is used.
Formula Used At highest point,
$\text{T +}\,\text{mg = }\dfrac{\text{m}{{\text{v}}^{\text{2}}}}{\text{r}}$
or, $\text{T = }\dfrac{\text{m}{{\text{v}}^{2}}}{\text{r}}-\text{mg}$
Complete Step by Step Solution
Given:
$\begin{align}
& \text{m = 0}\text{.1 kg} \\
& \text{r = 1m} \\
& \text{v = }{5\text{m}}/{\text{sec}}\; \\
\end{align}$
As the body is rotated at the end of the string in a vertical circle,
At the highest point, the tension in the string and the weight of the body together provides the necessary centripetal force.
Therefore,
$\begin{align}
& \text{T +}\,\text{mg = }\dfrac{\text{m}{{\text{v}}^{\text{2}}}}{\text{r}} \\
& \text{T = }\dfrac{\text{m}{{\text{v}}^{2}}}{\text{r}}-\text{mg} \\
& =\dfrac{0.1\times 5\times 5}{1}-0.1\times 10 \\
& =2.5-1 \\
& \text{T = 1}\text{.5 N} \\
\end{align}$
Tension in the string at the highest point is 1.5 N (option C)
Note: If the body is at lowest point, then a part of tension ${{\text{T}}_{1}}$ balances the weight of the body and the remaining part provides the necessary centripetal force. Hence, formula used will be${{\text{T}}_{1}}-\text{mg = }\dfrac{\text{m}{{\text{v}}^{2}}}{\text{r}}$
The conditions when the body is at highest point and at the lowest point must be understood properly so as to solve the problem correctly.
Formula Used At highest point,
$\text{T +}\,\text{mg = }\dfrac{\text{m}{{\text{v}}^{\text{2}}}}{\text{r}}$
or, $\text{T = }\dfrac{\text{m}{{\text{v}}^{2}}}{\text{r}}-\text{mg}$
Complete Step by Step Solution
Given:
$\begin{align}
& \text{m = 0}\text{.1 kg} \\
& \text{r = 1m} \\
& \text{v = }{5\text{m}}/{\text{sec}}\; \\
\end{align}$
As the body is rotated at the end of the string in a vertical circle,
At the highest point, the tension in the string and the weight of the body together provides the necessary centripetal force.
Therefore,
$\begin{align}
& \text{T +}\,\text{mg = }\dfrac{\text{m}{{\text{v}}^{\text{2}}}}{\text{r}} \\
& \text{T = }\dfrac{\text{m}{{\text{v}}^{2}}}{\text{r}}-\text{mg} \\
& =\dfrac{0.1\times 5\times 5}{1}-0.1\times 10 \\
& =2.5-1 \\
& \text{T = 1}\text{.5 N} \\
\end{align}$
Tension in the string at the highest point is 1.5 N (option C)
Note: If the body is at lowest point, then a part of tension ${{\text{T}}_{1}}$ balances the weight of the body and the remaining part provides the necessary centripetal force. Hence, formula used will be${{\text{T}}_{1}}-\text{mg = }\dfrac{\text{m}{{\text{v}}^{2}}}{\text{r}}$
The conditions when the body is at highest point and at the lowest point must be understood properly so as to solve the problem correctly.
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