Question

A rod of length 20 cm is made of metal . It expands by 0.075 cm when its temperature is raised from $0^{\circ} C$ to $100^{\circ} C$ . Another rod of a different metal B having the same length expands by 0.045 cm for the same change in temperature . A third rod of the same change in temperature . A third rod of the same length is composed of two parts , one of metal A and the other of metal B. This rod expands by 0.060 cm for the same change in temperature . The portion made of metal A has the length :

• A. 20 cm
• B. 10 cm
• C. 15 cm
• D. 18 cm

Answer 1

Answer: (B)

10 cm

Answer 2

Let $l _{1}$ be the length of potion of metal $A$ and $l _{2}$ be the length of portion of metal $B$. Thus $l_{1}+l_{2}=20 cm$ For the given change in temperature, change in length $\propto$ intial length of rod. Hence $\Delta l _{1}=0.075 \frac{ l _{1}}{20}$ And $\Delta l _{2}=0.045 \frac{ l _{2}}{20}$ Thus $\Delta l _{1}+\Delta l _{2}=0.060$ Solving for $l_{1}$ gives $l_{1}=10 cm$