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Physics

(a) A truck and a car are running with the same speed on a highway. If the ratio of the kinetic energies is 25 : 12, then what is the ratio of their masses?

(b) Give two examples in which mechanical energy is conserved.

Work, Energy & Power

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Answer

(a) Let kinetic energy of truck be KEt and that of car be KEc and v be their common speed.

Given,

KEtKEc=2512\dfrac{\text{KE}\text{t}}{\text{KE}\text{c}} = \dfrac{25}{12}

By formula,

KE = 12\dfrac{1}{2} mv2

⇒KEtKEc=2512⇒12mtv212mcv2=2512⇒mtmc=2512\phantom{\Rightarrow} \dfrac{\text{KE}\text{t}}{\text{KE}\text{c}} = \dfrac{25}{12} \\[1em] \Rightarrow \dfrac{\dfrac{1}{2}\text{m}\text{t}\text{v}^2}{\dfrac{1}{2}\text{m}\text{c}\text{v}^2} = \dfrac{25}{12} \\[1em] \Rightarrow \dfrac{\text{m}\text{t}}{\text{m}\text{c}} = \dfrac{25}{12}

Hence, ratio of masses = 25 : 12

(b) Mechanical energy is conserved in:

  1. Simple pendulum and
  2. Motion of a freely falling body.

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