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Units and Measurements question

2022 · 27 Jul · Shift 1 · Q47
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  5. /2022 · 27 Jul · Shift 1 · Q47

Units and Measurements question

2022 · 27 Jul · Shift 1 · Q47

JEE MainPhysicsUnits and MeasurementsMCQ+4 / −1
A torque meter is calibrated to reference standards of mass, length and time each with 5%5 \%5% accuracy. After calibration, the measured torque with this torque meter will have net accuracy of :
  1. A
    15%
  2. B
    25%
  3. C
    75%
  4. D
    5%
View written solutionFree

Correct answer: B

  1. Write the dimensional formula of torque

Torque is τ=force×distance\tau = \text{force} \times \text{distance}τ=force×distance

Since [force]=[MLT−2],[\text{force}] = [M L T^{-2}],[force]=[MLT−2], we get [τ]=[ML2T−2].[\tau] = [M L^2 T^{-2}].[τ]=[ML2T−2].

So torque depends on:

  • mass with power 111
  • length with power 222
  • time with power −2-2−2
  1. Use the rule for maximum percentage error

If a quantity Q=AaBbCc,Q = A^a B^b C^c,Q=AaBbCc, then the maximum percentage error is ΔQQ×100=(∣a∣ΔAA+∣b∣ΔBB+∣c∣ΔCC)×100.\frac{\Delta Q}{Q} \times 100 = \left(|a|\frac{\Delta A}{A} + |b|\frac{\Delta B}{B} + |c|\frac{\Delta C}{C}\right) \times 100.QΔQ​×100=(∣a∣AΔA​+∣b∣BΔB​+∣c∣CΔC​)×100.

Here each reference standard of mass, length, and time has 5%5\%5% error.

Thus for torque: Δττ×100=1(5%)+2(5%)+2(5%).\frac{\Delta \tau}{\tau} \times 100 = 1(5\%) + 2(5\%) + 2(5\%).τΔτ​×100=1(5%)+2(5%)+2(5%).

  1. Calculate

5%+10%+10%=25%.5\% + 10\% + 10\% = 25\%.5%+10%+10%=25%.

  1. Final answer

Hence the net accuracy/error in measured torque is 25%.\boxed{25\%}.25%​.

So the correct option is B.

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