Question

A string is wrapped round a log of wood and it is pulled witha force $F$ as shown in the figure. Choose the correct statement (s).
I Tension $T$ in the string decrease with increase in $\theta$
II Tension $T>F$ if $\theta >\pi /3$

• A. Only I is true
• B. both are true
• C. only II is true
• D. both are wrong

Answer 1

The correct option is C only II is true

$\begin{array}{c}2T\cos \theta =F\\ T=\frac{F}{2\cos \theta }\\ Tincreasewithincreasein\theta \\ T>F\\ \Rightarrow \frac{F}{2\cos \theta }>F\\ \Rightarrow 2\cos \theta <1\\ \cos \theta <\frac{1}{2}\\ \theta >\frac{\pi }{3}\end{array}$

Ans. (C)