Question

A ride in amusement park Imagica consists of rotating circular platform of $6m$ in diameter, from which heavy seats are suspended at end of light chains (length of chain $=3m$). When the system rotates, chains make an angle of ${37}^{\circ }$ with vertical. Find speed of kid sitting on it.

• A. $6m/s$
• B. $14m/s$
• C. $18m/s$
• D. $12m/s$

Answer 1

The correct option is A $6m/s$

$Tcos\theta =mg$
$Tsin\theta =mr{w}^2$
$tan\theta =\frac{r{w}^2}{g}=\frac{4.8\times w^2}{10}$
$\frac{3}{4}=\frac{4.8w^2}{10}$
$w^2=\frac{100}{4\times 16}$
$w=1.25$
($r=3+3sin{37}^0=3+3\times 0.6$
$=3+1.8=4.8$)

$v=rw=4.8\times 1.25=6m/s$