A solid sphere of mass 500 g and radius 10 cm
rolls without slipping with the velocity
20 cm/s. The total kinetic energy of the sphere
will be
a) 0.014j b) 0.028j c) 280j d)140j
Answers
Answer:
v = 20 cm / s = 0.02 m / s.
Now , v = 0.02 m / s ;
hence , k.e. = 1 / 2 m × v^2
= 1 / 2 × 0.5 kg × 0.02 × 0.02
= 0.0001 Joules.
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The total kinetic energy of solid sphere is 0.014 J hence option (a) is correct choice.
A solid sphere of mass 500g and radius 10 cm rolls without slipping with the velocity 20 cm/s.
We have to find the total kinetic energy of the sphere
We know,
Total kinetic energy = translational kinetic energy + rotational kinetic energy
= 1/2 mv² + 1/2 Iω²
Where
- m is mass of sphere,
- v is velocity ,
- I is moment of inertia of sphere about centre of mass
- and ω is angular velocity.
for solid sphere, I = 2/5 mr²
Now, Total kinetic energy = 1/2 mv² + 1/2 (2/5 mr²)ω²
= 1/2 mv² + 1/5 mr²ω²
= 1/2 mv² + 1/5 m(ωr)²
for rolling without slipping, v = ωr
= 1/2 mr² + 1/5 mv²
= 7/10 mv²
Here, m = 500 g = 0.5 kg , v = 20 cm/s = 0.2 m/s
= 7/10 (0.5)(0.2)²
= 7 × 0.02/10
= 0.014 J