(1) Comparison of a certain quantity with a standard quantity of the same nature (that is unit) is called

(a) Measurement                           (b) dimension                     (c) scale                           (d) analysis

(2) The standard physical quantity with which other quantities of the same nature are compared for measurement is called

(a) Dimensions                                 (b) unit                           (c) measurement              (d) scale

(3) Which one is not a unit of time?

(a) Light Year                    (b) Year                (c) Day                  (d) century

(4)The angle subtended at the center of a circle by an arc of length equal to the radius of the circle is

(a) 10                     (b) one radian                  (c) one steradian               (d) one minute

(5) The solid angle subtended by an area of the sphere equal to the square of its radius is

(a) 10                     (b) one radian                    (c) one steradian             (d) one minute

(6) The angle subtended at the center of a circle by an arc equal to 1/360 of the circumference of the circle is called

(a) 10                    (b) one radian                    (c) one steradian               (d) one minute

(7) The 60th part of one degree angle is called

(a) 10                     (b) one radian                    (c) one steradian               (d) one minute

(8) The circumference of a circle is given by

(a) 4/3 πr3            (2) 2πr                                 (c) 4πr2                                (d)4/3 πr2

(9) Number of radii in the circumference of a circle is

(a) π                      (b) ½ π                  (c) 2π                   (d) none of these

Solution:             Length of the circumference = 2πr

(Where r is the radius of the circle)

Number of radii in the circumference = 2πr/r = 2π

(Note: Since 1 radius length subtends an angle of 1 rad, therefore, number of radians in a circle is also 2π)

(10) A complete circle subtends an angle in radians at its center

(11) The relation between degrees and radians is

(a) 1 rad = 1800                  (b) 1 rad = 57.30                              (c) 1 rad = 33.30                 (d) 1 rad = 10

Solution:             A complete circle has number of degrees = 360

A complete circle has number of radians = 2π = 2*3.14 = 6.28

One radian has number of degrees = 360/6.28 = 57.3

(12) 10 expressed in radians is

(a) 57.3 rad                        (b) 1/57.3 rad                    (c) 57.3π rad                      (d) none of these

(13) The angle made in radians by the minute’s hand of a watch in 30 minutes is

(a) π rad               (b) ½ π rad                                         (c) 2π rad                            (d) none of these

Solution:             Circumference of a circle (watch) = 2π radians

½ Circumference of a circle = ½ * 2π = π radians

Since half the circumference of a watch is 30 minutes go of the minute’s hand, therefore, during 30 minutes, the minute’s hand of the watch will make an angle of π rad.

(14) The angle made in degrees by the minute’s hand of a watch in 15 minutes is

(a) 300                  (b) 450                                 (c) 900                                 (d) 1200

(Can you do it yourself!)

(15) A sphere has radius of 10 cm. The angle subtended by 300 cm2 of its area at the center is

(a) 3 steradian                  (b) 3π steradian                 (c) 3 radian                         (d) none of these

Solution:             Radius = 10 cm                 Square of the radius = 100 cm2

Now by definition 100 cm2 of the surface area of the sphere subtends a solid angle of 1 steradian. Therefore, 300 cm2 of the surface area will subtend a solid angle of 3 steradians.

(16) A sphere has a radius of 5 cm. The angle subtended at the center by an area of 25 cm2 is

(a) 250                  (b) 1/25 rad                        (c) 1 steradian                                 (d) none of them

(Do it yourself)