Units and Measurement

The errors in the measurement which arise due to unpredictable fluctuations in temperature and voltage supply are:

The radius of a sphere is measured to be (7.50±0.85) cm. Suppose the percentage error in its volume is x. The value of x, to the nearest integer, is.

The time period of a simple pendulum is given by T = 2π√(l/g). The measured value of the length of pendulum is 10cm known to a 1 mm accuracy. The time for 200 oscillations of the pendulum is found to be 100 second using a clock of 1 s resolution. The percentage accuracy in the determination of 'g' using this pendulum is 'x'. The value of 'x' to the nearest integer is,

The vernier-scale used for measurement has a positive zero error of 0.2 mm. If while taking a measurement it was noted that '0' on the vernier-scale lies between 8.5 cm and 8.6 cm, vernier coincidence is 6, then the correct value of measurement is …………… cm. (least count = 0.01 cm)

A physical quantity z depends on four observables a, c, c and d, as z = (a²b³)/(√cd³). The percentages of error in the measurement of a, b, c and d are 2%, 1.5%, 4% and 2.5% respectively. The percentage of error in z is:

A student measuring the diameter of a pencil of circular cross-section with the help of a vernier scale records the following four readings 5.50 mm, 5.55 mm, 5.45 mm; 5.65 mm. The average of these four readings is 5.5375 mm and the standard deviation of the data is 0.07395 mm. The average diameter of the pencil should therefore be recorded as:

A quantity X is given by (IFv²MLL⁴) in terms of moment of inertia I, force F, velocity v, work W and Length L. The dimensional formula for x is same as that of:

Dimensional formula for thermal conductivity is (here K denotes the temperature):