Question

Two cylinders having radii $2R$ and $R$ and moment of inertia $4I$
and $I$ about their central axes are supported by axles perpendicular to their planes. The large cylinder is initially rotating clockwise with angular velocity ${\omega }_0$. The small cylinder is moved to the right until it touches the large cylinder and is caused to rotate by the frictional force between the two. Eventually slipping ceases and the two cylinders rotate at constant rates in opposite direction.

• A. $\frac{{\omega }_0}{4}$
• B. ${\omega }_0$
• C. $\frac{{\omega }_0}{2}$
• D. $\frac{{\omega }_0}{8}$

Answer 1

The correct option is B ${\omega }_0$

As there is no slipping at the contact point $⟹w_{1}R=w_2\left(2R\right)$

$w_1=2w_2$ ...........(a)

Also, $fR=I{\alpha }_1$ and $f\left(2R\right)=4I{\alpha }_2$

$⟹{\alpha }_1=2{\alpha }_2$ ..................(b)

$w_1=0+{\alpha }_{1}t$ ............(c)

$w_2=w_o-{\alpha }_{2}t$

Using (a) and (b), $\frac{w_1}{2}=w_o-\frac{{\alpha }_1}{2}t$ ............(d)

Solving c and d, gives $w_1=w_o$