# NCERT Physics Class 11 Exemplar Chapter 2 Units And Measurements Part-4

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30). If the unit of force is 100 N, unit of length is 10 m and unit of time is 100 s, what is the unit of mass in this system of units?

Explanation:

31). Give an example of

(a) a physical quantity which has a unit but no dimensions.

Explanation: Angle or solid angle

(b) a physical quantity which has neither unit nor dimensions.

Explanation: Relative density, etc.

(c) a constant which has a unit.

Explanation: Planck’s constant, universal gravitational constant, etc.

(d) a constant which has no unit.

Explanation: Reynold number

32). Calculate the length of the arc of a circle of radius 31.0 cm which

subtends an angle of at the center.

Explanation:

33). Calculate the solid angle subtended by the periphery of an area of 1cm2 at a point situated symmetrically at a distance of 5 cm from the area.

Explanation:

34). The displacement of a progressive wave is represented by , where x is distance and t is time. Write the dimensional formula of

35). Time for 20 oscillations of a pendulum is measured as . What is the precision in the measurements? What is the accuracy of the measurement?

Explanation: (a) Precision is given by the least count of the instrument.

For 20 oscillations, precision = 0.1 s

For 1 oscillation, precision = 0.005 s.

(b) Average time

36). A new system of units is proposed in which unit of mass is α kg, unit of length β m and unit of time γ s. How much will 5 J measure in this new system?

Explanation: Since energy has dimensions of ML2 T –2, 1J in new units becomes . Hence 5 J becomes .

37). The volume of a liquid flowing out per second of a pipe of length l and radius r is written by a student as where P is the pressure difference between the two ends of the pipe and η is co efficient of viscosity of the liquid having dimensional formula Check whether the equation is dimensionally correct.

Explanation: The dimensional part in the expression is Therefore, the dimensions of the right hand side comes out to be , which is volume upon time. Hence, the formula is is dimensionally correct.

38). A physical quantity X is related to four measurable quantities a, b, c and d as follows:

. The percentage error in the measurement of a, b, c and d are 1%, 2%, 3% and 4%, respectively. What is the percentage error in quantity X? If the value of X calculated on the basis of the above relation is 2.763, to what value should you round off the result.

Explanation: The fractional error in X is

Since the error is in first decimal, hence the result should be rounded off as 2.8.

39). In the expression P = E l 2 m–5 G–2, E, m, l and G denote energy, mass, angular momentum and gravitational constant, respectively. Show that P is a dimensionless quantity.

Explanation: Since E, l and G have dimensional formulas:

Hence, will have dimensions:

Thus, P is dimensionless.

40). If velocity of light c, Planck’s constant h and gravitational constant G are taken as fundamental quantities then express mass, length and time in terms of dimensions of these quantities.

Explanation: M, L, T, in terms of new units become