This and the following three questions relate to the same situation: A uniform d

Question

This and the following three questions relate to the same situation:

A uniform disk of unknown mass M and radius R = 10 cm is free to rotate about its axis. A light cord is wrapped around the rim on the disk and then tied to a small can of mass m = 50 gm. The cord does not slip as it unwinds on the disk. When released the can moves down with acceleration 3.27 m/s2. Take g = 9.81 m/s2.

What is the angular acceleration of the disk?

(a)   0 rad/s2
(b)   8.2 rad/s2
(c)   65.4 rad/s2
(d)   16.4 rad/s2
(e)   32.7 rad/s2

QUESTION 2

What is the tension in the string?

(a)   0 N
(b)   0.164 N
(c)   1.308 N
(d)   0.327 N
(e)   0.654 N

QUESTION 3

What is the mass of the disk?

(a)   0.8 kg
(b)   0.2 kg
(c)   0.4 kg
(d)   0.1 kg
(e)   0.6 kg

Explanation / Answer

part a )

angular acceleration = a/r

a = 3.27

r = 10cm

alpha = 3.27/10x 10^-2 = 32.7 rad/s^2

Qns 2 )

mg - T = ma

T = m(g-a)

T = 0.3265 N = 0.327 N

Qns 3 )

F * R = I*alpha

mg * R = 1/2 * M*R^2 * a/R

mg = 1/2 * M*a

M = 2mg/a

M = 0.2996 = 0.2 kg

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