Assertion: When percentage error in the meansurement of mass and velocity are `1%` and `2%` respectively the percentagwe error in K.E. is `5%`.
Reason: `(Delta K)/(K) = (Delta m)/(m) = (2 Delta v )/(v)`.

Options

A. If both assertion and reason are true and reason is the correct explation of assertion.
B. If both assertion but reason is not the correct explanation of assertion.
C. If assertion is true but reason is false.
D. If both assertion and reason are false.

Answer

a

Explanation

Kinetic energy `K = (1)/(2) mv^(2)`
Taking log on both sides
In `K = (1)/(2) + "In" m + 2 "in" v`
Differentiating both we get
or `(Delta K)/(K) = (Delta m)/(m) + 2 (Delta v )/(v) `
`(Delta K)/(K)xx 100 = (Delta m)/(m) xx 100 + 2 xx (Delta v)/(v)xx 100 `
`= 1% = (2 xx 2%) = 3%`