Question

The moment of inertia of a solid flywheel about its axis is $0.1kg{m}^2$. A tangential force of 2 kg wt. is applied round the circumference of the flywheel with the help of a string and mass arrangement as shown in the figure. If the radius of the wheel is 0.1 m, find the acceleration of the mass

• A. $163.3rad{s}^{-2}$
• B. $16.3rad{s}^{-2}$
• C. $81.66rad{s}^{-2}$
• D. $8.16rad{s}^{-2}$

Answer 1

Answer: (B)

Suppose a be the linear acceleration of the mass and T the tension in the string.
Hence,
$Mg-T=Ma...(i)$
Let $\alpha$ be the angular acceleration of the flywheel. The couple applied to the flywheel is
$I\alpha =TR$ or $T=\frac{I\alpha }{R}...\left(ii\right)$
Now we know that $a=R\alpha ...\left(iii\right)$
Putting $\left(ii\right)$ and $\left(iii\right)$ in eq. $\left(i\right),$ we get
$Mg=\frac{I\alpha }{R}=MR\alpha$
$\therefore \alpha =\frac{MgR}{I+M{R}^2}...\left(iv\right)$
$=\frac{2\times 9.8\times 0.1}{0.1+2\times {\left(0.1\right)}^2}=16.33rad{s}^{-2}$