Question

.A uniform rod of mass m and length l is hanging with the help of two strings as shown in the figure-

If T₁ and T₂ be tensions in the strings, then-

• A. $T_1>T_2$
• B. $T_1<T_2$
• C. $T_1+T_2=mg$
• D. $T_1=T_2$

Answer 1

Answer: (B), (C)

$T_1+T_2=mg$

For translatory equilibrium:

force is caused due to the tension force alone
$\Rightarrow T_1+T_2=mg$

For rotational equilibrium:
when the string is in rotary equilibrium about the Centre of Mass

$$\begin{gathered} \mathrm{Torque}\mathrm{is}\mathrm{compensted} \\ (\mathrm{i}.\mathrm{e}){\mathrm{T}}_1{\mathrm{r}}_1={\mathrm{T}}_2{\mathrm{r}}_2 \\ \mathrm{here}\mathrm{as}{\mathrm{r}}_1>{\mathrm{r}}_2,\mathrm{it}\mathrm{is}\mathrm{the}\mathrm{tension}{\mathrm{T}}_2\mathrm{which}\mathrm{counters}\mathrm{and}\mathrm{brings}\mathrm{equilllibrium} \\ \mathrm{Thus},{\mathrm{T}}_2>{\mathrm{T}}_1 \end{gathered}$$

Hence option (a) and (d) are correct answers