Question

A solid sphere of mass 4.0 kg and radius of 0.12 m is at rest at the top of a ramp inclined 150. It rolls to the bottom without slipping. The upper end of the ramp is1.2 m higher than the lower end. What is the linear speed of the sphere when it reaches the bottom of the ramp?

4.1 m/s is the correct answer.

Answer 1

Given

mass of the sphere m = 4 kg

radius of the sphere   r = 0.12 m

angle of incline   θ =   15 ^o

height of ramp h = 1.2 m

    from law of conservation of energy

               mgh   = ( 1/2) m v^ 2 + ( 1/2) I ω^2

                        = (1/2) m v ^2   + ( 1/2) I ( v ^2 / r ^2 )

                         =  (1/2) m v ^2    +( 1/2) ( 2/5 m r ^2   ) (v ^2 / r ^2 )

                         = ( 1/2) m v ^2 ( 1 + 2 /5 )

                 gh    = 0.5 v ^2 ( 1.4 )

   speed of sphere    v ^2 = gh / 0.5 *1.4

                               v   = √ 9.8*1.2 /0.5*1.4

                                     = 4.098 m/s

Answer 2

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