Question

A light string is wrapped round a cylindrical log of wood which is placed on a horizontal surface with its axis vertical and it is pulled with a constant force F as shown in figure ( friction is absent everywhere)

Answer 1

Final Answer: (A) & (C)

Q : A light string is wrapped round a cylindrical log of wood which is placed on a horizontal surface with its axis vertical and it is pulled with a constant Force F as shown in figure . (Friction is absent everywhere)

Steps:

1) Let the Tension in the string be T.

Since, the system is in Equilibrium .

∴ F(Left) =F(right)

$Tcos(\theta)+Tcos(\theta)= F \\=>2Tcos(\theta)= F \\ => T=\frac{F}{2cos(\theta)}$

2) Since, $cos(\theta)$ is decreasing function.

So,T will increase with increase in $\theta$ . (A)

$3)\:\theta\ \textgreater \ \frac{\pi}{3} \\ =\ \textgreater \ cos(\theta)\ \textless \ cos(\frac{\pi}{3}) \\ =\ \textgreater \ cos(\theta) \ \textless \ \frac{1}{2} \\ =\ \textgreater \ \frac{F}{2T} \ \textless \ \frac{1}{2} \\ =\ \textgreater \ F\ \textless \ T$

Similarly, when $\theta< \frac{\pi}{3}$ ,then T<F.

Hence, Option (C) is also right and (d) is wrong.

Finally ,(A) & (C) is right.