Equal torques act on the discs A and B of the previous problem, i… - Vidyadip

Question

Equal torques act on the discs A and B of the previous problem, initially both being at rest. At a later instant, the linear speeds of a point on the rim of A and another point on the rim of B are v_A and v_B respectively. We have:

v_A> v_B
v_A= v_B
v_A < v_B
The relation depends on the actual magnitude of the torques.

✓

Answer

v_A> v_B

Explanation:

$\tau=\text{I}\alpha$ (Magnitude)

For equal torque, we have:

$\text{I}_{\text{A}\propto\text{A}}=\text{I}_{\text{B}\propto\text{B}}$

$\text{I}_{\text{A}}<\text{I}_{\text{B}}$

$\Rightarrow\alpha_{\text{A}}>\alpha_{\text{B}}\ \dots(\text{i})$

Now, $\omega=\alpha\text{t}$

Or, $\frac{\text{v}}{\text{r}}=\alpha\text{t}$

$\text{v}_{\text{A}}>\text{v}_{\text{B}}$ [Using (i)]

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