Question

Thin uniform rod of mass $3kg$ and length $2m$ starts from rest and rotate about an axis passing through its centre and perpendicular to its length with a speed $600rpm$ in $10sec$ then torque acting on it is:

• A. $3.14Nm$
• B. $9.42Nm$
• C. $6.28Nm$
• D. $12.56Nm$

Answer 1

The correct option is C $6.28Nm$

Moment of inertia of the uniform rod about its centre

$I=\frac{M{L}^2}{12}$

$I=\frac{3\times 2^2}{12}$

$I=1kg{m}^2$

Now angular acceleration of the rod is given by

$\alpha =\frac{600}{60}\times \frac{2\pi }{10}$

$\alpha =2\pi rad/s^2$

Torque acting on the rod

$\tau =I\alpha$

$\tau =2\pi Nm$

$\tau =6.28Nm$