To what temperature (in °C) must a cylindrical rod of one metal 10.083 mm in diameter and a plate of second metal having a circular hole 9.987 mm in diameter have to be heated for the rod to just fit into the hole? Assume that the initial temperature is 27°C and that the linear expansion coefficient values for metals one and two are 4.0 x 10-6 (°C)-1 and 16 x 10-6 (°C)-1, respectively.

834°C

Explanation:

By setting the equation of final diameter of one metal and another metal equal to one another in order to determine final temperature, the equation for final diameter is given by,

=(1 + α(-))

=

9.987(1 + 16 x (-27)) = 10.083( 1 + (4 x )(-27))

9.987(1 +  16 x - 432 x ) = 10.083( 1 + 4 x - 108  x )

9.987 + 1.59 x - 4.31 x = 10.083 + 4.033  x - 1.088 x

1.59 x - 4.033  x = 10.083-1.088 x - 9.987+4.31 x

1.187 x = 0.099

= 0.099/ 1.187 x

= 834°C

diagram is missing, but i will try to explain your doubt.

answer:

amplitude is the maximum displacement or distance moved on a point of a vibrating body or wave measured from its equilibrium position.it is equal to half the length of vibration path.