Answer:
The expression to obtain the radius of the smaller pulley is r = 0.559*R
If I have the value of R I will be able to calculate the value of r, but in the exercise you do not give it, so I leave the expression.
Explanation:
The tangential components of acceleration at points A and B is equal to zero
[tex]a_{A} =a_{B} =0[/tex]
The acceleration of points A and B are:
[tex]a_{A} =\frac{V^{2} }{r} \\a_{B} =\frac{V^{2} }{R}[/tex]
Where
V = velocity of the tape
r = radius of the small pulley
R = radius of the large pulley
[tex]\frac{a_{A} }{a_{B} } =\frac{\frac{V^{2} }{r} }{\frac{V^{2} }{R} } \\1.79=\frac{V^{2}R}{V^{2}r } \\r=0.559*R[/tex]
