Question

If there is 2 error in mass and 3 error in velocity then find error in kinetic energy error

Answer 1

Answer:

Explanation:

Hello Dear.

Kinetic Energy(K) = 1/2 × mv²

where, m = mass of the body and v = velocity.

Now, Obtaining the Formula in terms of the Momentum.

∵ p = mv

⇒ v = p/m

∴ K = 1/2 × m (p/m)²

⇒ K = p²/2m

⇒ p² = K × 2m  

Now, Solving the Question.

∵ p² = K × 2m  

∴ Taking Logarithms on both the sides of the above equation.

log p² = log( k 2m)

⇒ 2log p = log K + log 2m  

⇒ log K = 2 log p - log 2m

Now, Differentiating the both sides of the Equation,

∴ dK/K = 2(dp/p) - dm/m

∴ |dK/K|max. = 2|2/100| + |-3/100|

⇒ |dK/K| = 2 × 0.02 + 0.03

⇒ |dK/K|max. = 0.07

∴ Maximum % Error in the Kinetic Energy K is 0.07 × 100 % = 7%.