AP EAMCET · PHYSICS · Laws of Motion
A stone of mass \(2 \mathrm{~kg}\) tied to a light inextensible string of length \(\frac{5}{3} \mathrm{~m}\) is whirling in a circular path in a vertical plane. If the ratio of the maximum tension to the minimum tension in the string is 4 , then the speed of the stone at the highest point of the circle is \(\left(g=10 \mathrm{~ms}^{-2}\right)\)
- A \(20 \mathrm{~ms}^{-1}\)
- B \(10 \sqrt{3} \mathrm{~ms}^{-1}\)
- C \(\sqrt{50} \mathrm{~ms}^{-1}\)
- D \(10 \mathrm{~ms}^{-1}\)
Answer & Solution
Correct Answer
(C) \(\sqrt{50} \mathrm{~ms}^{-1}\)
Step-by-step Solution
Detailed explanation
Tension is maximum at bottom of vertical circle and it is \( T_1=\frac{m v^2}{r}+m g \) Tension is minimum at top and it is \( T_2=\frac{m u^2}{r}-5 m g \) Given, ratio \(\frac{T_1}{T_2}=4 \Rightarrow 21 m g=3 \frac{m u^2}{r}\) \( \Rightarrow \quad u^2=7 \mathrm{rg} \) Now,…
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