Question

Q3. A solid sphere of mass 4.0 kg and radius 0.12 m starts from rest at the top of a ramp inclined 15°, and rolls to the bottom. The upper end of the ramp is 1.2 m higher than the lower end. What is the linear speed of the sphere when it reaches the bottom of the ramp? (Take: g = 9.8 m/s²)

Answer 1

Answer:

The Answer Is 4.098 m/s.

Explanation:

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