A uniform hollow cylinder having mass m and radius r has a massless string wound over it. One end of sting is attached to a mass m. If during the motion the string does not slip on the cylinder, and the mass falls with an acceleration a (in `cm//s^2`) on release then give your answer as: `a/100`. (Take `g = 9.8 m//s^(2)`)

Answer

D

Explanation

Acceleration, `a = ralpha`…….(i)
Torque, `tau = Ialpha`……….. (ii)
and `tau = r xx F = r xx T`………. (`therefore F = T`) ……….(iii) G From equation (ii) and (iii),
`mr^(2) alpha = rT`……….. `(1 = mr^(2)), therefore T = mr alpha`
T = ma............... [From (i) ....... (iv)]

From the above diagram,
`mg - T = ma, therefore mg - ma = ma`............ [From (iv)]
`therefore 2ma = mg, therefore a = g/2`
`= 980/2`........... (`therefore g = 9.8 m//s^(2) = 980 cm//s^(2)`)
`therefore a = 490 cm//s^(2)`