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A disc without slipping rolls down a hill of vertical height 1000 cm. If the disc starts from rest at the top of the hill, what is its magnitude of velocity at the bottom?

Solution

Theory: The disc is placed at the top of a hill of height 1000 cm = 10 m. It posses potential energy which is converted to kinetic energy as it rolls down. The motion of the disc during rolling down is of two types; linear and rotational and hence do the kinetic energy. As the P.E is converted to K.E (without slipping means there is no friction and all the potential energy is converted to  kinetic energy), therefore,

Loss in potential energy = Gain in kinetic energy

Given                        Height = 10 m               vi = 0 m/s             g = 9.8 m/s2

Required                  vf =?

Now P.E = mgh, therefore,

Putting these values,

Putting the values

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