Question

1 a- A thick cylinder of inner radius 10 cm and outer radius 50 cm rolls at 4 m/s without slipping. If the cylinder has a mass of 10 kg, what is its linear kinetic energy?
Optional Answers:

1. 80 J
2. 41.6 J 3. 121.6 J 4. 0 J

b- A thick cylinder of inner radius 10 cm and outer radius 50 cm rolls at 4 m/s without slipping. If the cylinder has a mass of 10 kg, what is its rotational kinetic energy?
Optional Answers:

1. 0 J
2. 80 J
3. 121.6 J 4. 41.6 J

c- A thick cylinder of inner radius 10 cm and outer radius 50 cm rolls at 4 m/s without slipping. If the cylinder has a mass of 10 kg, what is its total kinetic energy?
Optional Answers:

1. 121.6 J 2. 80 J
3. 41.6 J 4. 0 J

Answer 1

Here we have given as,

R1 = 10cm

R2 = 50 cm

Mass =10 kg

Velocity V = 4 m/s

1.

Here the linear kinetic energy will be given as,

K.E = 0.5 MV² = 0.5 × 10 × 40^2 = 80 J

Hence option 1)80 J is correct here.

2.

Here the moment of inertia of the cylindrical body is given as

I = 0.5 M (R1²+R2²)

And rotational kinetic energy is given as,

KE = 0.5 I × w²

But here the angular velocity will = Vcm/r

But Vcm = 0

Hence rotational kinetic energy will be as,

I = 0

Hence option 1z) 0J

3. Now total kinetic energy will be sum of the linear and rotational kinetic energy

So that

K.E total = KEl + KER = 80 J

Hence option 2) 80 J si correct answer here.