A yo-yo of mass is modeled as a rigid cylinder of radius with rotational inertia…

PHYSICS · Single correct · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion

Problem

A yo-yo of mass

m

is modeled as a rigid cylinder of radius

R

with rotational inertia

I

about its central axis. It is released from rest and descends a vertical distance

h

while the string unwinds without slipping around its rim. Which of the following gives the speed

v

of the yo-yo’s center of mass after it has descended the distance

h

? (a)

v = \sqrt{\dfrac{2gh}{1+\dfrac{I}{m R^{2}}}}

(b)

v = \sqrt{2 g h}

(c)

v = \sqrt{\dfrac{2 m g h}{m - I/R^{2}}}

(d)

v = \sqrt{\dfrac{2 m g h}{m + 2 I/R^{2}}}