Students A , B and C measure the length of a room using 25   m long measuring tape of least count ( LC ) 0 . 5   cm , meter-scale of LC 0 . 1   cm and a foot-scale of LC 0 . 05   cm , respectively. If the specified length of the room is 9 . 5   m , then which of the following students will report the lowest relative error in the measured length?

Step-by-step solution

Student A : Length of scale = 25   m Least count = 0 . 5   cm = 0 . 005   m Student A can measure the length of 9 . 5   m by using the scale only once so there will be an error of 0 . 005   m in 9 . 5   m ∴  Relative error  = 0 . 005 9 . 5 = 0 . 0005 Student B : Length of scale : 1   m = 100   cm Least count = 0 . 05   cm To measure 9 . 5   m , student B has to use this meter scale atleast 10 times ∴ Relative error  = 0 . 05 100 × 10