Question

The mass of scooter and bike are in the ratio 2:3 but moving with the same speed of 108 km/h . Computer the ratio of their kinetic energy.

Answer 1

Let the mass of scooter (m₁) be 2y and mass of bike(m₂) be 3y, then
speed of bike and scooter = 108 km/h = 30 m/s
Kinetic energy of scooter/ kinetic energy of bike = 

=1/2 x m₁ x v² / 1/2 x m₂ x v²  
= m₁/m₂
= 2y / 3y
= 2/3
= 2 : 3

∴ The ratio of kinetic energy of scooter to bike is 2 : 3.

Answer 2

Mass of Scooter = 2x

Mass of Bike = 3x

​Speed = velocity, v = 108 km/h

v = 108 x 5/18 m/s

v = 30 m/s

K.E. of Scooter = 1/2 x m x [v]^2

=1/2 x 2x x [30]^2

= 1/2 x 2x x 900

= 2x x 450

= 900x J

K.E. of Bike = 1/2 x m x [v]^2

= 1/2 x 3x x [30]^2

= 1/2 x 3x x 900

= 3x x 450

= 1350x J

Ratio of kinetic energies of Scooter and Bike = 900x J / 1350x J

= 900 / 1350

= 90 / 135

= 18 / 27

= 2 / 3

Hence , the ratio of the kinetic energies of the Scooter and Bike is 2 : 3.