Question

A block of mass 2kg hangs from the rim of a wheel of radius 0.5m. On releasing from rest the block falls through 5m height in 2s. The moment of inertia of the wheel will be

• A. $1kg-m^2$
• B. $3.2kg-m^2$
• C. $2.5kg-m^2$
• D. $1.5kg-m^2$

Answer 1

The correct option is D $1.5kg-m^2$

$Tr=I\alpha$
$r^{2}T=I\alpha r$
$r^{2}T=Ia$ (1)
$mg-T=ma$ (2)
$5=\frac{1}{2}a(2{)}^2$ (3)
$\left(2\right)$ and$\left(3\right)$ in $\left(1\right)$ gives
$\Rightarrow I=1.5kg{m}^2$