Consider a metal scale of length `30cm` and an object. The scale is calibrated for temp `20^(@)C`.
(a) What is the actual length of division which is shown as `1cm` by scale at `40^(@)C`. Given `alpha_(s) = 2 xx 10^(-5)//"^(@)C`.
(b) What will be the reading of scale at `40^(@)C` if the actual length of objects is `10cm`.
(c ) What will be the actual length of object at `40^(@)C` if is measured length is `10cm`.
(d) What is `%` error in measurement for part (b) and (c).
(e) If the linear expansion coefficient of object is `alpha_(0) = 4 xx 10^(-5)` and neglecting the expansion of scale, then answers of (b) and (c) parts.
(f) If `alpha_(0) = 4 xx 10^(-5)` and `alpha_(s) =2xx 10^(-5)` then find answers of (b) and (c) part.

Explanation

(a) `l = 1{1 + 2 xx 10^(-5) xx 20}`
(b) `l = 10 {1 -4 xx 10^(-4)}`
(c ) `l = 10 {1+ 4 xx 10^(-4)}`
(d) `% l_(1) =- 4 xx 10^(-2)%`
`%l_(2) = (-4 xx 10^(-2))/(1+4 xx 10^(-4)) % ~= -4 xx 10^(-2) %`
(e) `l_(1) = 10 {1+ 20 xx4 xx 10^(-5)}`
`l_(2) = 10 {1-20 xx 4 xx 10^(-5)}`
(f) `l_(1) = 10 {1+40 xx 10^(-5)}`
`l_(2) = 10 {1 - 40 xx 10^(-5)}`