Two spheres P and Q, each of mass 200 g are attached to a string of length one metre as shown in the figure.…
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 hor i zon tal
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)
$\frac{1}{2}$
$\frac{2}{3}$
$\frac{3}{2}$
$\frac{2}{1}$
Solution
Tension between $P$ and $Q$ is
$T_1=$ centripetal force on $Q=m r \omega^2$
$
=200 \times 1 \times \omega^2\left(\mathrm{~g} \cdot \mathrm{m} \cdot \frac{\mathrm{rad}^2}{\mathrm{~s}^2}\right)
$
Tension between $O$ and $P$ is
$T_2=$ centripetal force on $Q+$ centripetal force on $P$
$=200 \times 1 \times \omega^2+200 \times \frac{1}{2} \times \omega^2$
$=300 \times 1 \times \omega^2\left(\mathrm{~g} \cdot \mathrm{m} \cdot \frac{\mathrm{rad}^2}{\mathrm{~s}^2}\right)$
Ratio of tension is
$\frac{T_1}{T_2}=\frac{200 \times 1 \times \omega^2}{300 \times 1 \times \omega^2}=\frac{2}{3}$
