Question

Two spheres $P$ and $Q$, each of mass $200\, g$ are attached to a string of length one metre as shown in the figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant angular speed. The ratio of the tension in the string between $P$ and $Q$ to that of between $P$ and $O$ is $(P$ is at mid-point of the line joining $O$ and $Q$ )

• A. $\frac{1}{2}$
• B. $\frac{2}{3}$
• C. $\frac{3}{2}$
• D. $\frac{2}{1}$

Answer 1

Answer: (B)

$\frac{2}{3}$

Answer 2

Tension between $P$ and $Q$ is
$T_{1}=$ centripetal force on $Q=m r \omega^{2}$
$=200 \times 1 \times \omega^{2}\left( g \cdot m \cdot \frac{ rad ^{2}}{ s ^{2}}\right)$
Tension between $O$ and $P$ is
$T_{2}=$ centripetal force on $Q+$ centripetal force on $P$
$=200 \times 1 \times \omega^{2}+200 \times \frac{1}{2} \times \omega^{2}$
$=300 \times 1 \times \omega^{2}\left( g \cdot m \cdot \frac{ rad ^{2}}{ s ^{2}}\right)$
Ratio of tension is
$\frac{T_{1}}{T_{2}}=\frac{200 \times 1 \times \omega^{2}}{300 \times 1 \times \omega^{2}}=\frac{2}{3}$