Question

The moment of inertia of a solid flywheel about its axis is $0.1 \,kg\, m^2$. 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. $163.3\, rad\, s^{-2}$
• B. $16.3\, rad\, s^{-2}$
• C. $81.66\, rad\, s^{-2}$
• D. $8.16\, rad\, s^{-2}$

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 $α$ 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 $a = Rα \,...\left(iii\right)$
Putting $\left(ii\right)$ and $\left(iii\right)$ in eq. $\left(i\right),$ we get
$Mg=\frac{I\alpha}{R}=MR\alpha$
$\therefore \alpha=\frac{MgR}{I+MR^{2}}\,...\left(iv\right)$
$=\frac{2\times9.8\times0.1}{0.1+2\times\left(0.1\right)^{2}}=16.33\,rad\,s^{-2}$