Question

A certain bicycle can go up on a gentle incline with a constant speed. If the frictional force of the ground pushing the rear wheel is $F_2=4\text{N}$, then what pulling force $F_1$ must the chain apply on the sprocket wheel if $R_1=30\text{m}$ and $R_2=5\text{m}$?

• A. $4\text{N}$
• B. $24\text{N}$
• C. $140\text{N}$
• D. $\frac{35}{4}\text{N}$

Answer 1

The correct option is B $24\text{N}$

$\because$ Speed of the wheel is constant that means angular velocity $\left(\omega \right)$ is constant and angular acceleration $\alpha =0$
Net torque on the wheel must be zero about its centre of mass.
i.e ${\tau }_{\text{net}}=0$
Considering anticlockwise sense of rotation to be $+ve$ :
$-\left(F_1{R}_2\right)+F_2{R}_1=0$
[torques are in opposite directions]
$\Rightarrow -(F_1\times 5)+(F_2\times 30)=0$
Substituting $F_2=4\text{N}$,
$\therefore F_1=\frac{30\times 4}{5}=24\text{N}$