Question

In figure (i), half of the meter scale is made of wood while the other half of steel. The wooden part is pivoted at $O$ and a force $F$ is applied at the end of steel part. In figure (ii), the steel part is pivoted at $O$ and the same force is applied at the wooden end.

• A. More angular acceleration will be produced in (i)
• B. More angular acceleration will be produced in (ii)
• C. Same angular acceleration will be produced in both the conditions
• D. Information is incomplete

Answer 1

The correct option is B More angular acceleration will be produced in (ii)


In the given sitution SOM will shifted little bit towards the Still (because of heavier mass).
Let the distane from initial point to SOM is $r_1$ and $r_2$ respectively.

So, torque at rod 1: ${\tau }_1=F\times l-Mg{r}_1$ ..(1)
torque at rod 2: ${\tau }_2=F\times l-Mg{r}_2$ ..(2)
eq. (1)= eq. (2)
${\tau }_1={\tau }_2$


here, because $r_1>r_2$ so, ${\tau }_1<{\tau }_2$ ...(3)

Calculation of moment of inertia of each rod
using eq. (3) $I_1{\alpha }_1<I_2{\alpha }_2$

and for the above condition,
$I_1>I_2$ and ${\alpha }_1<{\alpha }_2$

Hence, option B is correct.