Measurement questions | form five Physics

State the law of dimensional analysis.

If the speed ​ V of the transverse wave along a wire of tension, ​ T and mass, ​ m is given by . Apply dimensional analysis to check whether the given expression is correct or not.

1. The force ‘F’ acting on an object of mass ‘m’, travelling at velocity ‘V’ in a circle of radius ‘r’ is given by; . If the measurements are recorded as: m =(3.5±0.1) kg, V = (20±1) m/s, r = (12.5±0.5) m; find the maximum possible;

1. Fractional error.
2. Percentage error in the measurement of force.

2. Show how you will record the reading of force, ‘F’, in part (a)

(i) Define the term dimensions of a physical quantity.
(ii) Identify two uses of dimensional equations.

(i) What is the basic requirement for a physical relation to be correct?
(ii) List two quantities whose dimension is [​ ML²​ ​T^-1​ ​ ].

The frequency ‘f’ of vibration of a stretched string depends on the tension ‘F’, the length ‘l’ and the mass per unit length of the string. Derive the formula relating the physical quantities by the method of dimensions.

Use dimensional analysis to prove the correctness of the relation , where by =density of the earth, g = acceleration due to gravity, R = radius of the earth and G= gravitational constant.

The number of particles n crossing a unit area perpendicular to ​ x-axis in a unit time is
given as where and are the number of particles per unit volume for the values of and respectively. What are the dimensions of diffusion constant ​ D?

The frequency, ​ ‘f’ of a vibrating string depends upon the force applied, ​ F the length, ​ ‘l’ of the string and the mass per unit length, μ. Using dimension show how ​ ‘f’ ​ is related to ​ F , ​ ​ l ​ and μ.

1. What is meant by least count of a measurement?
2. The period of oscillation of a simple pendulum is given by where by 100 vibrations were taken to measure 200 seconds. If the least count for the time and length of a pendulum of 1m are 0.1sec and 1mm respectively, calculate the maximum percentage error in the measurement of g.