Question

A length $L=15cm$ of flexible tape is tightly wound. It is then allowed to unwinding as it rolls down a fixed inclined that makes an angle $\theta ={30}^{\circ }$ with the horizontal, the upper end of the tape being fixed. Find the time taken (in second) by the tape to unwind completely. Neglect radius at any time w.r.t. the length of the rope.

Answer 1

Acceleration of rolling object is given by $a=\frac{g\sin \theta }{1+K}$
For disc $K=0.5$
Also given, $\theta ={30}^o$
Acceletation $a=\frac{10\times \sin {30}^o}{1+0.5}=\frac{10\times 0.5}{1.5}=\frac{10}{3}m/s^2$
Using $S=ut+\frac{1}{2}a{t}^2$
where $u=0$ and $S=15cm=0.15m$
$\therefore$ $0.15=0+\frac{1}{2}.\frac{10}{3}{t}^2$
$⟹t=0.3s$