Search any question & find its solution
Question:
Answered & Verified by Expert
A uniform rod of length $\ell$, mass $\mathrm{m}$ is hung from two strings of equal length from a ceiling as shown in figure. Determine the tensions in the strings?
Options:
Solution:
1356 Upvotes
Verified Answer
The correct answer is:
$\mathrm{mg} / 3$
Let us assume that tension in left and right string is $T_A$ and $T_B$ respectively.
The rod is in equilibrium, then $\vec{F}_{\text {net }}=0$ and $\vec{\tau}_{\text {net }}=0$
$\begin{aligned}
& \text { From, } \vec{F}_{\text {net }}=0 \\
& \mathrm{mg}=\mathrm{T}_{\mathrm{A}}+\mathrm{T}_{\mathrm{B}} \ldots
\end{aligned}$
$\begin{aligned}
& \text { From } \tau_{\text {net }}=0 \text { about } A, \\
& \mathrm{mg} \frac{1}{2}-\frac{31}{4} T_B=0 \\
& \Rightarrow T_B=\frac{2 \mathrm{mg}}{3}
\end{aligned}$
So, from eq. (1),
$\begin{aligned}
& \mathrm{T}_{\mathrm{A}}+\frac{2 \mathrm{mg}}{3}=\mathrm{mg} \\
& \Rightarrow \mathrm{T}_{\mathrm{A}}=\frac{\mathrm{mg}}{3}
\end{aligned}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.