Rotational Motion Question 217
Question: A tangential force of 20 N is applied on a cylinder of mass 4 kg and moment ofinertia $0.02kgm^{2}$ about its own axis. If the cylinder rolls without slipping, then linear acceleration of its centre of mass will be
Options:
A) $6.7m/s^{2}$
B)$10m/s^{2}$
C) $3.3m/s^{2}$
D)None of these
Show Answer
Answer:
Correct Answer: A
Solution:
[a] Let friction force = f $F+f=ma$- (i) $(F-f)R=I\alpha $- (ii) $
From $eq^{n}s.$ (i) and (ii),
$2F=ma+\frac{I\alpha }{R}$
$Use\alpha =\frac{a}{R}$(for pure rolling)
$2F=ma+\frac{Ia}{R^{2}}$ $40=4a+\frac{0.02a}{{{(0.1)}^{2}}};$
$a=\frac{40}{6}=6.7m/s^{2}$
