Question

9) A lightweight object and a very heavy object are sliding with equal speeds along a level frictionless surface. They both slide up the same frictionless hill. Which rises to a greater height?Select one:A. The light object, because it has smaller kinetic energy.B. The heavy object, because it has greater kinetic energy.C. The heavy object, because it weighs more.D. They both slide to the same height.E. The lightweight object, because it weighs less.

Answer 1

The kinetic energy of any object is,

`K=(1)/(2)mv^2`

where m is the mass, v is the velocity,

The potential energy of the same object at height h is,

`U=\text{mgh}`

where m is the mass, g is the acceleration due to gravity, h is the height,

By the law of conservation of energy,

`\begin{gathered} K=U \\ (1)/(2)mv^2=\text{mgh} \\ v^2=2gh \\ h=(v^2)/(2g) \end{gathered}`

As the value of height depends upon the velocity and acceleration due to gravity which is same for both the heavy and light object.

Thus, they both slide to the same height.

Hence, option D is the correct answer.