Q. No.A physical quantity \(Q \) depends on other physical quantities \(a, b\) and \(c\) as \(Q=\dfrac{a^4 b^3}{c^2}.\) If the maximum percentage error in measurement of \(a. b\) and \(c\) are \(3\%, 4\%\) and \(5\%\) respectively, then the maximum percentage error in measurement of \(Q\) is:
1. \(34\%\)
2. \(40\%\)
3. \(32\%\)
4. \(45\%\)
1. \(34\%\)
2. \(40\%\)
3. \(32\%\)
4. \(45\%\)
Subtopic: Â Errors |
 91%
Level 1: 80%+
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Pressure on a circular plate is obtained by measuring the force and the radius of the plate. If the error in measuring force and radius is \(1\%\) and \(0.5\%\) respectively, then the error in pressure is:
1. \(1\%\)
2. \(2\%\)
3. \(6\%\)
4. \(8\%\)
1. \(1\%\)
2. \(2\%\)
3. \(6\%\)
4. \(8\%\)
Subtopic: Â Errors |
 88%
Level 1: 80%+
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If the error in the measurement of mass is \(0.8\%\) and in volume it is \(0.4 \%,\) then the error in the measurement of density is:
1. \(1.2 \%\)
2. \(0.4 \%\)
3. \(0.8\%\)
4. \(1 \%\)
1. \(1.2 \%\)
2. \(0.4 \%\)
3. \(0.8\%\)
4. \(1 \%\)
Subtopic: Â Errors |
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Level 1: 80%+
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Two resistances, \(R_1=(60\pm6)~\Omega\) and \(R_2=(40\pm2)~\Omega\) are connected in series. The equivalent resistance will be:
1. \(100\pm12~\Omega\)
2. \(100\pm10~\Omega\)
3. \(100\pm8~\Omega\)
4. \(100\pm4~\Omega\)
1. \(100\pm12~\Omega\)
2. \(100\pm10~\Omega\)
3. \(100\pm8~\Omega\)
4. \(100\pm4~\Omega\)
Subtopic: Â Errors |
 88%
Level 1: 80%+
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If the error in measurement of the radius of a sphere is \(0.1\%,\) then the error in its volume will be:
1. \(0.3\%\)
2. \(0.4\%\)
3. \(0.5\%\)
4. \(0.6\%\)
Subtopic: Â Errors |
 87%
Level 1: 80%+
AIPMT - 1999
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Voltage and resistance for a resistor are measured as \(V=200 \pm 5\) volts and \(R=20 \pm 0.2~ \Omega.\) The percentage error in current \(I=\dfrac{V}{R} \text { is } x \text {. }\)Then the value of \(10x\) is:
1. \(45\)
2. \(35\)
3. \(30\)
4. \(60\)
1. \(45\)
2. \(35\)
3. \(30\)
4. \(60\)
Subtopic: Â Errors |
 86%
Level 1: 80%+
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The power generated in a circuit is given by \(P=i^2R,\) where \(i\) is current and \(R\) is resistance. The percentage errors in measuring \(i\) and \(R\) are \(0.3\) and \(0.5\) respectively. The maximum error in measuring power is
1. \(0.3\%\)
2. \(0.5\%\)
3. \(0.8\%\)
4. \(1.1\%\)
Subtopic: Â Errors |
 85%
Level 1: 80%+
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A physical quantity, \(y=\dfrac{a^{4} b^{2}}{\left(c d^{4}\right)^{1 / 3}}\) has four observables \(a,\) \(b,\) \(c\) and \(d.\) The percentage error in \(a,\) \(b,\) \(c\) and \(d\) are \(2\text{%},\) \(3\text{%},\) \(4\text{%}\) and \(5\text{%}\) respectively. The error in \(y\) is:
| 1. | \(6\text{%}\) | 2. | \(11\text{%}\) |
| 3. | \(12\text{%}\) | 4. | \(22\text{%}\) |
Subtopic: Â Errors |
 85%
Level 1: 80%+
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The angular momentum of a rotating sphere of mass-\(m,\) radius-\(r\) is computed from the expression: \(L=\dfrac25mr^2\omega,\) where \(\omega\) is the angular speed of rotation. The mass is known to within \(0.5\%,\) the radius to \(0.5\%,\) and the angular speed \((\omega)\) to within \(1\%.\) The fractional error in \(L\) is:
1. \(1\%\)
2. \(1.5\%\)
3. \(2\%\)
4. \(2.5\%\)
1. \(1\%\)
2. \(1.5\%\)
3. \(2\%\)
4. \(2.5\%\)
Subtopic: Â Errors |
 85%
Level 1: 80%+
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While measuring the acceleration due to gravity by a simple pendulum, a student makes a positive error of \(1\%\) in the length of the pendulum and a negative error of \(3\%\) in the value of time period. His percentage error in the measurement of \(g\) by the relation \(g=4\pi^2(l/T^2)\) will be
1. \(2\%\)
2. \(4\%\)
3. \(7\%\)
4. \(10\%\)
Subtopic: Â Errors |
 84%
Level 1: 80%+
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