A mas m hangs with help of a string wraped around a pulley on a frictionless bearling. The pulley has mass m and radius R. Assuming pulley to be a perfect uniform circular disc, the acceleration of the mass m, if the string does not slip on the pulley, is:

Options

A. `g`
B. `(2)/(3)g`
C. `(g)/(3)`
D. `(3)/(2)g`

Answer

b

Explanation

Let `T` be the tension in the string `alpha` be the angular acceleration of pulley and a be the linear downward acceleration of mass m
Troque on pulley `tau = T xx R , tau = I alpha`
where `I` = moment of linertia of pulley `= (mR^(2))/(2)`
`:. TR = I alpha = (mR^(2))/(2) (a)/(R) ( :' a = alpha R)`
or `T = (ma)/(2)`
Taking equation of motion of mass m we have
`mg -T = ma`
or `mg - (ma)/(2) = ma `
or `a = (2)/(3) g`
.