MHT CET · Physics · Work Power Energy
A simple pendulum has length \(2 \mathrm{~m}\) and a bob of mass 100 gram. It is whirled in a horizontal plane. If the string breaks under a tension of \(10 \mathrm{~N}\), the angle made by the string with vertical is \(\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\right)\)
- A \(\cos ^{-1}(0 \cdot 4)\)
- B \(\cos ^{-1}(0 \cdot 1)\)
- C \(\cos ^{-1}(0 \cdot 05)\)
- D \(\cos ^{-1}(0 \cdot 2)\)
Answer & Solution
Correct Answer
(B) \(\cos ^{-1}(0 \cdot 1)\)
Step-by-step Solution
Detailed explanation
A simple pendulum has a length of \(2 \mathrm{~m}\) and a bob of mass of \(100\mathrm{~grams}\). It is whirled in a horizontal plane. If the string breaks under a tension of \(10 \mathrm{~N}\), the angle made by the string with vertical is \(\cos ^{-1}(0.1)\).
\(\left(g=10 \mathrm{~m} / \mathrm{s}^{2}\right)\)
\(\mathrm{L}=2 \mathrm{~m}\)
\(\mathrm{~m}=\frac{100}{1000}=0.1 \mathrm{~kg}\)
\(\operatorname{Tcos} \Phi=m g\)
\(\operatorname{Tsin} \Phi=\frac{m v^{2}}{R}\)
\(\cos \Phi=\frac{m g}{T}=\frac{0.1 \times 10}{10}=0.1\)
\(\therefore \Phi=\cos ^{-1}(0.1)\)
\(\left(g=10 \mathrm{~m} / \mathrm{s}^{2}\right)\)
\(\mathrm{L}=2 \mathrm{~m}\)
\(\mathrm{~m}=\frac{100}{1000}=0.1 \mathrm{~kg}\)
\(\operatorname{Tcos} \Phi=m g\)
\(\operatorname{Tsin} \Phi=\frac{m v^{2}}{R}\)
\(\cos \Phi=\frac{m g}{T}=\frac{0.1 \times 10}{10}=0.1\)
\(\therefore \Phi=\cos ^{-1}(0.1)\)
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