Question

In given figure, pulley having radius, $r=1\text{m}$ and moment of inertia $I=2{\text{kgm}}^2$ about its axis of rotation. If $T_1=4\text{N}$ and $T_2=2\text{N}$ are the tension in the strings. Find the angular acceleration of pulley. (Take anti-clockwise rotation +ve)

• A. $2{\text{rad/s}}^2$
• B. $1{\text{rad/s}}^2$
• C. $4{\text{rad/s}}^2$
• D. $3{\text{rad/s}}^2$

Answer 1

The correct option is B $1{\text{rad/s}}^2$

F. B. D of Pulley


Net torque on Pulley about axis of rotation
${\tau }_{net}=(T_1-T_2)r$
(Taking anticlockwise rotation +ve)

$\Rightarrow {\tau }_{net}=(4-2)\times 1$
$=2\text{Nm}$

Given: $(I=2{\text{kg-m}}^2)$
We also know,
$\tau =I\times \alpha$
$\therefore {\tau }_{net}=I\times \alpha$
$\Rightarrow \alpha =\frac{{\tau }_{net}}{I}=\frac{2}{2}=1{\text{rad/s}}^2$