Question

A hollow sphere of radius 0.5 m and mass
10 kg, rolls on a horizontal surface. Its centre of
mass has speed 60 cm/s. Magnitude of work
required to stop it is
(1) 3 J (2) 5 J
(3) 1.8 J (4) 1.2 J

Answer 1

Explanation:

Given A hollow sphere of radius 0.5 m and mass 10 kg, rolls on a horizontal surface. Its centre of mass has speed 60 cm/s. Magnitude of work required to stop it is

Mass of hoop = 10 kg

Radius = 0.5 m

Speed of centre of mass = 60 cm/s = 0.6 m/s

Work done by hoop to stop it will be total kinetic energy of the hoop

 So Δw  =K.E (rotation) + K.E (translation)

1/2 Iω^2 + 1/2 mv^2

Now moment of inertia of the hoop I = mω^2 and ω = v/r

So work done =  1/2 mr^2 x v^2 / r^2 + 1/2 mv^2

                    = mv^2

                     = 100 x (0.6)^2

                     = 100 x 0.36

                     = 36 Joule

So work required to stop will be 36 Joule