Units and Measurements

The density of a uniform cylinder is determined by measuring its mass m, length l and diameter d. The measured values of m, l and d are 97.42 0.02 g, 8.35 0.05 mm and 20.20 0.02 mm, respectively. Calculated percentage fractional error in is .

1. 0.63%
2. 0.82%
3. 0.72%
4. 0.25%

The percentage error in the calculated volume of a sphere, if there is 2% error in its diameter measurement, is .

1. 1
2. 2
3. 6
4. 8

In an experiment to determine the resistance of a given wire using Ohm's law, the voltmeter and ammeter readings are noted as 10 V and 5 A, respectively. The least counts of voltmeter and ammeter are 500 mV and 200 mA, respectively. The estimated error in the resistance measurement is .

1. 0.25
2. 2
3. 2.5
4. 0.18

The diameter of a wire measured by a screw gauge of least count 0.001 cm is 0.08 cm. The length measured by a scale of least count 0.1 cm is 150 cm. When a weight of 100 N is applied to the wire, the extension in length is 0.5 cm, measured by a micrometer of least count 0.001 cm. The error in the measured Young's modulus is 109 N/m2. The value of is . (Ignore the contribution of the load to Young's modulus error calculation)

1. 1.3
2. 1.65
3. 0.13
4. 0.25

The time period of a simple harmonic oscillator is T = 2 mk. Measured value of mass (m) of the object is 10 g with an accuracy of 10 mg and time for 50 oscillations of the spring is found to be 60 s using a watch of 2 s resolution. Percentage error in determination of spring constant (k) is %.

1. 3.43
2. 7.60
3. 3.35
4. 6.76

In an experiment the values of two spring constants were measured as k1 = (10 0.2) N/m and k2 = (20 0.3) N/m. If these springs are connected in parallel, then the percentage error in equivalent spring constant is :

1. 1.33%
2. 2.67%
3. 1.67%
4. 2.33%

A spherical body of radius r and density falls freely through a viscous liquid having density and viscosity and attains a terminal velocity v0. Estimated maximum error in the quantity is : (Ignore errors associated with , and g, gravitational acceleration)

1. 2 [ rr - v0v0 ]
2. 2 [ rr + v0v0 ]
3. 2 rr + v0v0
4. 2 rr - v0v0

A quantity Q is formulated as X-2Y+ 32Z- 25. X, Y, and Z are independent parameters which have fractional errors of 0.1, 0.2, and 0.5, respectively in measurement. The maximum fractional error of Q is

1. 0.6
2. 0.8
3. 0.7
4. 0.1