Question

A string is wrapped on a wheel of moment of inertia $0.2{\text{kg m}}^2$ and radius $10\text{cm}$ and passes over a light pulley to support a block of mass $2\text{kg}$ as shown in figure. Find the acceleration of the block.

• A. $0.89{\text{ms}}^{-2}$
• B. $1.12{\text{ms}}^{-2}$
• C. $0.69{\text{ms}}^{-2}$
• D. None

Answer 1

The correct option is A $0.89{\text{ms}}^{-2}$

Applying Newton's second law for the block,
$mg-T=ma$
$\Rightarrow 2a=2g-T....\left(1\right)$
And applying the rotational form of Newton's law for the pulley,
$T.r=I\alpha$
or $T=\frac{I}{r^2}a=\frac{0.2a}{(0.1{)}^2}=20a....\left(2\right)$
From equations (1) and (2),
$a=\frac{2g}{(2+20)}=0.89{\text{ms}}^{-2}$