Question

A bob B of mass 1 kg is suspended from the ceiling of a toy train as shown in the figure. The train oscillates simple harmonically in horizontal direction with angular frequency $\Theta =5rad/s$ and amplitude a =0.1 m. what is the ratio of maximum and minimum tensions in the string AB during the motion $(g=10{ms}^{-2}$&$tan{37}^{\circ }=3/4)$

• A. 2
• B. 3
• C. 4
• D. 1

Answer 1

Answer: (A)

2

$\begin{array}{c}\text{from given picture}\\ \begin{array}{cc}a={\omega }^{2}A,,& \omega =5\text{rad}/S\\ A=0.1m& \end{array}\\ \text{on}a=25\times \frac{1}{10}\\ \text{on}a=\frac{5}{2}\end{array}$

$\begin{array}{c}{T}_2\cdot \cos {37}^{\circ }=mg\\ \text{on}{T}_2\times \frac{4}{5}=10\\ \text{on}{T}_2=\frac{50}{4}\\ \text{from}\left(1\right)\text{and}\left(2\right)T_{1}max=10N\end{array}$

$\begin{array}{c}\text{again}\\ \begin{array}{c}5/2\times 1=T_2\times \frac{3}{5}-T_1\text{min}\\ T_{\text{Imin}}=\frac{50}{4}\times \frac{3}{5}-5/2=5\\ \therefore \frac{T_{1max}}{T_{1}min}=\frac{10}{5}=2\end{array}\end{array}$

Ans A