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

A physical quantity C is related to four other quantities p, q, r and s as follows C = pq2r3 s The percentage errors in the measurement of p, q, r and s are 1\%, 2\%, 3\% and 2\%, respectively. The percentage error in the measurement of C will be %

A physical quantity Q is related to four observables a, b, c, d as follows : Q= ab4cd where, a=(60 3) Pa; b=(20 0.1) m; c=(40 0.2) N s m-2 and d=(50 0.1) m, then the percentage error in Q is x1000, where x= .

The energy of a system is given as E(t)= 3e- t, where t is the time and =0.3 s-1. The errors in the measurement of and t are 1.2\% and 1.6\%, respectively. At t=5 s, maximum percentage error in the energy is :

1. 6\%
2. 11.6\%
3. 4\%
4. 8.4\%

The maximum percentage error in the measurement of density of a wire is [Given, mass of wire =(0.60 0.003) g radius of wire =(0.50 0.01) cm length of wire =(10.00 0.05) cm]

1. 7
2. 8
3. 5
4. 4

Young's modulus is determined by the equation given by Y = 49000 Ml dynecm2 where M is the mass and l is the extension of wire used in the experiment. Now error in Young modulus (Y) is estimated by taking data from M–l plot in graph paper. The smallest scale divisions are 5 g and 0.02 cm along load axis and extension axis respectively. If the value of M and l are 500 g and 2 cm respectively then percentage error of Y is :

1. 2%
2. 0.02%
3. 0.5%
4. 0.2%

To find the spring constant (k) of a spring experimentally, a student commits 2\% positive error in the measurement of time and 1\% negative error in measurement of mass. The percentage error in determining value of k is :

1. 5\%
2. 3\%
3. 1\%
4. 4\%

The radius (r), length (l) and resistance (R) of a metal wire was measured in the laboratory as r=(0.35 0.05) cm R=(100 10) ohm l=(15 0.2) cm The percentage error in resistivity of the material of the wire is :

1. 37.3\%
2. 25.6\%
3. 35.6\%
4. 39.9\%

If the percentage errors in measuring the length and the diameter of a wire are 0.1\% each. The percentage error in measuring its resistance will be:

1. 0.144%
2. 0.2%
3. 0.1%
4. 0.3%

The measured value of the length of a simple pendulum is 20 cm with 2 mm accuracy. The time for 50 oscillations was measured to be 40 seconds with 1 second resolution. From these measurements, the accuracy in the measurement of acceleration due to gravity is N%. The value of N is:

1. 6
2. 5
3. 4
4. 8

The resistance R= VI where V=(200 5) V and I=(20 0.2) A, the percentage error in the measurement of R is :

1. 5.5%
2. 3%
3. 7%
4. 3.5%

A physical quantity Q is found to depend on quantities a, b, c by the relation Q= a4b3c2. The percentage error in a, b and c are 3\%, 4\% and 5\% respectively. Then, the percentage error in Q is :

1. 43%
2. 34%
3. 66%
4. 14%