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 is : (take $g=10m{s}^{-2}$)

• 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 $1.5kg{m}^2$

$mg-T=ma$
$T\times r=I\alpha$
$a=r\alpha$

$mg-\frac{I\alpha }{r}=mr\alpha$

$5=\frac{1}{2}a{t}^2$

$5=\frac{1}{2}\times a\times 4$

$a=\frac{5}{2}$

$\alpha =\frac{5}{2r}$

$mg-\frac{I\times 5}{2r^2}=m\left(\frac{5}{2}\right)$

$20-10I=5$

$I=\frac{15}{10}$$=1.5kg{m}^2$