Question

A cord is wound around the circumference of a bicycle wheel (without tyre) of diameter $1m$. A mass of $2kg$ is tied to the end of the cord and it is allowed to fall from rest. The weight falls $2m$ in $4s$. The axle of the wheel is horizontal and the wheel rotates with its plane vertical. The angular acceleration produced is:

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

• A. $0.5rad{s}^{-2}$
• B. $1rad{s}^{-2}$
• C. $2rad{s}^{-2}$
• D. $4rad{s}^{-2}$

Answer 1

The correct option is A $0.5rad{s}^{-2}$

We first find the linear acceleration a by using the relation-
$s=ut+\frac{1}{2}a{t}^2$
or
$2=0+\frac{1}{2}\times a\times 4^2$
which gives $a=\frac{1}{4}m/s^2$
Now $R=0.5m$.

The angular acceleration $\alpha$ is given by:
$\alpha =\frac{a}{R}=\frac{1}{4\times 0.5}=\frac{1}{2}=0.5rad/s^2$