Question

A string is wrapped around the rim of a wheel of moment of inertia $0.20kgm^{2}$ and of radius $20cm$ . The wheel is free to rotate about its axis and initially it is at rest. The string is now pulled by a force of $20N$ . The angular velocity of the string after $5s$ will be

• A. $90rads^{- 1}$
• B. $70rads^{- 1}$
• C. $95rads^{- 1}$
• D. $100rads^{- 1}$

Answer 1

Answer: (D)

We know that $\tau=I\alpha ...\left(\right.i\left.\right)$
and $\tau=rF=\left(\frac{20}{100}\right)\left(\right.20\left.\right)$
$\tau=4Nm$
Now from eq. $\left(\right.i\left.\right)$
$4=\left(\right.0.2\left.\right)\left(\right.\alpha \left.\right)$
So $\alpha =20rads^{- 2}$
So from $\omega =\omega _{0}+αt$
$\omega _{0}=0andt=5sec.$
So $\omega =0+20\left(\right.5\left.\right)$
$\omega =100rad/sec.$