If the percentage error in the measurement of momentum and mass of an object are 2 % and 3 % respectively, then maximum percentage error in the calculated value of its kinetic energy is

Question

If the percentage error in the measurement of momentum and mass of an object are 2 % and 3 % respectively, then maximum percentage error in the calculated value of its kinetic energy is (A) 2 % (B) 1 % (C) 5 % (D) 7 %

Tardigrade Admin · Accepted Answer

KE =( text Momentum / text Mass )=(p2/2 m) (Δ K/K) × 100 % =((2 Δ p/p) × 100) %+((Δ m/m) × 100) % =2 × 2 %+3 % (Δ K/K) × 100 % ⇒ 7 %

Q. If the percentage error in the measurement of momentum and mass of an object are $2%$ and $3%$ respectively, then maximum percentage error in the calculated value of its kinetic energy is

$2%$

$1%$

$5%$

$7%$

$K E = \frac{Momentum}{Mass} = \frac{p ^{2}}{2 m}$
$\frac{Δ K}{K} \times 100% = (\frac{2Δ p}{p} \times 100) % + (\frac{Δ m}{m} \times 100) %$
$= 2 \times 2% + 3%$
$\frac{Δ K}{K} \times 100% \Rightarrow 7%$

Q. If the percentage error in the measurement of momentum and mass of an object are 2% and 3% respectively, then maximum percentage error in the calculated value of its kinetic energy is

2%

1%

5%

7%