Question

A triangular plate of uniform thickness and density is made to rotate about an axis perpendicular to the plane of the paper and (a) passing through A, (b) passing through B, by the application of some force F at C (mid-point of AB) as shown in fig. In which case is angular acceleration more

• A. in case $\left(a\right)$
• B. in case $\left(b\right)$
• C. both $\left(a\right)$ and $\left(b\right)$
• D. none of these

Answer 1

The correct option is B in case $\left(b\right)$

Let, I${}_a$ and I${}_b$ be the moment of inertia at A and B respectively.
And ${\alpha }_a$ and ${\alpha }_b$ be the angular velocities at A nd B respectively.
Let I be moment of inertial of triangular plate about its COM.
Since we know that in a triangle, COM is located at centriod.
Assume A is at origin and B is on X-axis and length of BD be c.Therefore , centroid is at ($\frac{2b}{3},\frac{c}{3}$).
$I_a=I+M\ast (AG{)}^2$ {where ,G is centroid}
$I_b=I+M\ast (BG{)}^2$
By comparing $I_a$ and $I_b$ ,
$\Rightarrow I_a>I_b$------->1
considering Torque equation at both the axis,
F($\frac{b}{2}$)=$I_a{\alpha }_a$ and
F($\frac{b}{2}$)=$I_b{\alpha }_b$
$\Rightarrow$ $I_a{\alpha }_a$=$I_b{\alpha }_b$
By using 1,
$\Rightarrow {\alpha }_b>{\alpha }_a$