Question

lgs 2026

1 kg toryumdan elde edilen enerji ile \\(3,5 \cdot 10^6\\) kg kömürden elde edilen enerji birbirine eşittir. günümüz teknolojisinde \\(10^5\\) kg kömürden elde edilen enerji ile 80 adet elektrikli aracın enerji ihtiyacı karşılanmaktadır.

buna göre, 28 adet elektrikli aracın enerji ihtiyacını karşılamak için kaç kilogram toryum gereklidir?

a) \\(10^2\\) b) 10 c) \\(10^{-1}\\) d) \\(10^{-2}\\)

Explanation:

Identify the given relationships

We are given two primary equivalences:

1. The energy from \(1\text{ kg}\) of thorium is equal to the energy from \(3.5 \cdot 10^6\text{ kg}\) of coal:

$$1\text{ kg thorium} = 3.5 \cdot 10^6\text{ kg coal}$$

1. The energy from \(10^5\text{ kg}\) of coal meets the energy needs of \(80\) electric vehicles:

$$10^5\text{ kg coal} = 80\text{ vehicles}$$

Calculate coal needed for 28 vehicles

We use proportional reasoning to find the amount of coal, \(x\), required for \(28\) vehicles:

$$\frac{10^5\text{ kg coal}}{80\text{ vehicles}} = \frac{x}{28\text{ vehicles}}$$

$$x = \frac{28 \cdot 10^5}{80}\text{ kg coal}$$

$$x = \frac{28}{80} \cdot 10^5 = 0.35 \cdot 10^5 = 3.5 \cdot 10^4\text{ kg coal}$$

Convert coal to thorium

We find the equivalent amount of thorium, \(y\), for \(3.5 \cdot 10^4\text{ kg}\) of coal:

$$y = \frac{3.5 \cdot 10^4\text{ kg coal}}{3.5 \cdot 10^6\text{ kg coal/kg thorium}}$$

$$y = \frac{3.5}{3.5} \cdot \frac{10^4}{10^6}\text{ kg thorium}$$

$$y = 10^{-2}\text{ kg thorium}$$

Answer:

• (A) \(10^2\)
• (B) \(10\)
• (C) \(10^{-1}\)
• (D) \(10^{-2}\) (Correct answer)