A body of mass (5 ± 0.5) kg is moving with a velocity of (20 ± 0.4) m/s. Its kinetic energy will be (a) (1000 ± 140) J (b) (500 ± 0.14) J (c) (1000 ± 0.14) J (d) (500 ± 140) J

Answer: (a). K = 1/2mv² = 1/2(5)(20)² = 1000 J (Δ K)/(K) = (Δ m)/(m) + 2(Δ v)/(v) = 0.5/5 + 2·0.4/20 = 0.10 + 0.04 = 0.14 Δ K = 0.14 × 1000 = 140 J So the answer is (a) (1000 ± 140) J.

A body of mass (5 ± 0.5) kg is moving with a velocity of (20 ± 0.4)… | JEE Main 2023 (13 Apr, Shift 1)

Q69JEE Main 2023 · 13 APR · SHIFT 1Easy

Errors in Measurement

A body of mass $(5 \pm 0.5)\text{ kg}$ is moving with a velocity of $(20 \pm 0.4)\text{ m/s}$ . Its kinetic energy will be

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Answer: (a)

$K = \frac{1}{2}mv^2 = \frac{1}{2}(5)(20)^2 = 1000\text{ J}$
$\frac{\Delta K}{K} = \frac{\Delta m}{m} + 2\frac{\Delta v}{v} = \frac{0.5}{5} + 2\cdot\frac{0.4}{20} = 0.10 + 0.04 = 0.14$
$\Delta K = 0.14 \times 1000 = 140\text{ J}$
So the answer is (a) $(1000 \pm 140)\text{ J}$ .

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