Question

Two circular rods, one steel and the other copper, are both 0.755 mm long and 1.50 cm in diameter. Each is subjected to a force with magnitude 4250 N that compresses the rod. Use copper = 1.1*10¹¹ and steel = 2.0 * 10^11.  

What is the difference in the length of the two rods when compressed?

Express your answer in meters to two significant figures.

Answer is NOT 6.05 x 10^-5

Answer 1

Here we have given that,

Lenght = 0.755 mm

Diameter = 1.50 cm

force= 4250 N

Ycopper = 1.1*1011

and

Ysteel = 2.0 * 1011

Now we know that,

From Using formula of young modulus we will get,

E = Fl/AY

So that,

the difference in the length of the two rods when compressed will be as,

Difference Es-Ec = 4250×0.755×10^-3/0.0075²[(1/3.14×2×10¹¹)-1/3.14×1.1×10¹¹]

Difference in the length = 9.0835 ×10^-8 m

Which is our required answer.

Note:- notice here the length is given as in question in in mm so make sure that it is mm otherwise if it will come in m then answer will be changed accordingly which will given us as 9.0835×10^-5 m.