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i got a question in my M.C.Q test . the question and the given solution is being reproduced here

Use the following information to answer the next question.

Plastics are known to contract and expand with a decrease and increase in temperature (respectively). With every 5°C decrease in temperature, the length of a plastic rod decreases by 8 mm, and with every 5°C increase in temperature, its length increases by 10 mm.

A plastic rod was taken at room temperature. Its temperature was first lowered to 20°C below room temperature and its length was noted down. Its temperature was then increased to 15°C above room temperature and its length was again noted down.

What was the difference between the lengths of the rod that were noted down in the readings?

A :

18 mm

B :

20 mm

C :

62 mm

D :

64 mm

View Graph View Solutions

We begin by taking the length of the rod at room temperature as 0. Thus, a decrease in its length will be negative, while an increase in its length will be positive.

With every 5°C decrease in temperature, the length of the rod decreases by 8 mm or it changes by −8 mm.

Therefore, when the temperature is lowered to 20°C below the room temperature, change in length of the rod

With every 5°C increase in temperature, the length of the rod increases by 10 mm or it changes by +10 mm.

Therefore, when the temperature is lowered to 15°C above room temperature, change in length of the rod

Thus, the difference between the lengths noted down = [+30 − (−32)] mm

= (30 + 32) mm

= 62 mm

I AM NOT CONVINCED WITH THE ABOVE ANSWER AS

Let the length of rod is x mm at room temperature. when it's temperature decresed by 20 degree C, it's length will decrease by 32 mm i.e (x - 32) mm length is noted. Now it's temperature is increased by 15 degree above room temperature i.e increase in temperature shall be (20 + 15) = 35 degree C and now this will increase the length by 70 mm. then the final length noted shall be (x-32+70) mm. Thus the difference in the noted down readings shall be

(x-32+70) - (x-32) = 70 mm.and

Final change in length from room temperature shall be (x-32+70) - x = 38 mm

Meritnation Expert may please give comment.

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