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ICSE Class 10 Physics Question 21 of 27

Solved Sample Paper 4 — Question 9

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Question

Question 6(iii)

(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.

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.