The percentage errors in the measurement of mass and speed are 2% and 3% respectively. How much will be the maximum error in the estimate of kinetic energy obtained by measuring mass and speed?

Asked by anupchan2005 | 3rd Sep, 2021, 10:20: PM

Expert Answer:

Kinetic energy K = (1/2) m v2 .......................... (1)
 
where m is mass and v is velocity
 
By taking logarithm of eqn.(1) and by differentiating , we get
 
dK/K = (dm/m) + 2 (dv/v)
 
we are given that , dm/m = 0.02 and dv/v = 0.03
 
hence , dK/K = 0.02 + 2 ( 0.03) = 0.08
 
Hence maximum error in kinetic enregy is 8%

Answered by Thiyagarajan K | 3rd Sep, 2021, 11:44: PM