Question

A rope is wound around hollow cylinder of 3kg and radius 40cm if the rope is pulled downward with the force of 3newton find linear acceleration of rope.

Answer 1

Torque -

underset{ au }{

ightarrow}= underset{r}{

ightarrow} imes underset{F}{

ightarrow}    

 

- wherein

This can be calculated by using either   au=r_{1}F; or;  au=rcdot F_{1}

r_{1} = perpendicular distance from origin to the line of force.

F_{1} = component of force perpendicular to line joining force.

 

 

 

and,

 

Analogue of second law of motion for pure rotation -

vec{ au }=I, alpha

- wherein

Torque equation can be applied only about two point

(i) centre of motion.

(ii) point which has zero velocity/acceleration.

T=I \alpha

FR \sin \Theta=I \alpha

FR=I \alpha= \alpha = \frac{FR}{MR^{2}}

\alpha= \frac{30 \times 0.4}{2 \times (0.4)^{2}}\:\:\:\Rightarrow \alpha 25 rad/s^{2}  

 

Option 1)

0.25\: rad/s^{2}

This option is incorrect.

Option 2)

25\: rad/s^{2}

This option is correct.

Option 3)

5\: m/s^{2}

This option is incorrect.

Option 4)

25 m/s^{2}

This option is incorrect.