NCERT Solutions Class 6th Maths Chapter – 5 Understanding Elementary Shapes Exercise – 5.2

Question 1.What fraction of a clockwise revolution does the hour hand of a clock turn through, When it goes from-

(a) 3 to 9
(b) 4 to 7
(c) 7 to 10
(d) 12 to 9
(e) 1 to 10
(f) 6 to 3

Solution – 

(a) 3 to 9
9 – 3 = 6 ÷ 12 = 1/2 of a revolution

(b) 4 to 7
7 – 4 = 3 ÷ 12 = 1/4 of a revolution

(c) 7 to 10
10 – 7 = 3 ÷ 12 = 1/4 of a revolution

(d) 12 to 9 i.e., 0 to 9
9 – 0 = 9 ÷ 12 = 3/4 of a revolution

(e) 1 to 10
10 – 1 = 9 ÷ 12 = 3/4 of a revolution

(f) 6 to 3 i.e., 6 to 12 and then 12 to 3
6 to 12 = 12 – 6 = 6 and 12 to 3 = 0 to 3 = 3 – 0 = 3
6 + 3 = 9 ÷ 12 = 3/4 of a revolution

Question 2. Where will the hand of a clock stop if it-

(a) Starts at 12 and makes 1/2 of a revolution, clockwise?
(b) Starts at 2 and makes 1/2 of a revolution, clockwise?
(c) Starts at 5 and makes 1/4 of a revolution, clockwise?
(d) Starts at 5 and makes 3/4 of a revolution, clockwise?

Solution –

We know that one complete clockwise revolution, hour hand will rotate by 360⁰

(a) When hour hand of a clock starts at 12 and makes 1 / 2 revolution clockwise, it will rotate by 180⁰. Hence, the hour hand of a clock will stop at 6.

(b) When hour hand of a clock starts at 2 and makes 1 / 2 revolution clockwise, it will rotate by 180⁰ Hence, the hour hand of a clock will stop at 8.

(c) When hour hand of a clock starts at 5 and makes 1 / 4 revolution clockwise, it will rotate by 90⁰ Hence, hour hand of a clock will stop at 8.

(d) When hour hand of a clock starts at 5 and makes 3 / 4 revolution clockwise, it will rotate by 270⁰ Hence, hour hand of a clock will stop at 2.

Question 3. Which direction will you face if you start facing-

(a) east and make 1/2 of a revolution clockwise?
(b) east and make 1½ of a revolution clockwise?
(c) west and make 3/4 of a revolution anti- clockwise?
(d) South and make one full Revolution?
(Should we specify clockwise or anti- clockwise for this last question? Why not?)

Solution –

Taking one full revolution we will reach back to the original (starting) position Therefore, it make no difference whether we turn clockwise or anticlockwise.

Question 4. What part of a revolution have you turned through if you stand facing-

(a) east and turn clockwise to face north?
(b) south and turn clockwise to face east?
(c) west and turn clockwise to face east?

Solution –

(a) If we start from east and reach at north (turning clockwise) 3/4 of a revolution is required.

(b) If we start from south turning clockwise to face east, 3/4 of a revolution is required.

(c) If we start from west turning clockwise to face east, 1/2 of a revolution is required.

Question 5. Find the number of right angles turned through by the hour hand of a clock when it goes from-

(a) 3 to 6
(b) 2 to 8
(c) 5 to 11
(d) 10 to 1
(e) 12 to 9
(f) 12 to 6

Solution –

The hour hand of a clock revolves by 3600 or it covers 4 right angles in one complete revolution.

(a) If hour hand of a clock goes from 3 to 6, it revolves by 90⁰ or 1 right angle.

(b) If hour hand of a clock goes from 2 to 8, it revolves by 180⁰ or 2 right angles.

(c) If hour hand of a clock goes from 5 to 11, it revolves by 180⁰ or 2 right angles.

(d) If hour hand of a clock goes from 10 to 1, it revolves by 90⁰ or 1 right angle.

(e) If hour hand of a clock goes from 12 to 9, it revolves by 270⁰ or 3 right angles.

(f) If hour hand of a clock goes from 12 to 6, it revolves by 180⁰ or 2 right angles.

Question 6. How many right angles do you make if you start facing-

(a) south and turn clockwise to west?
(b) north and turn anti- clockwise to east?
(c) west and turn to west?
(d) south and turn to north?

Solution –

By revolving one complete round in either clockwise or anti-clockwise direction, we will revolve by 360⁰ and two adjacent directions are at 90⁰ away from each other.

(a) If we start facing towards South and turn clockwise to West, we have to make 1 right angle.

(b) If we start facing towards North and turn anti-clockwise to East, we have to make 3 right angles.

(c) If we start facing towards West and turn to West, we have to make one complete round or 4 right angles.

(d) If we start facing towards South and turn to North, we have to make 2 right angles.

Question 7. Where will the hour hand of a clock stop if it starts-

(a) from 6 and turns through 1 right angle?
(b) from 8 and turns through 2 right angles?
(c) from 10 and turns through 3 right angles?
(d) from 7 and turns through 2 Straight angles?

Solution –

We know that in 1 complete revolution in either clockwise or anticlockwise direction, hour hand of a clock will rotate by 360⁰ or 4 right angles.

(a) If hour hand of a clock starts from 6 and turns through 1 right angle, it will stop at 9.

(b) If hour hand of a clock starts from 8 and turns through 2 right angles, it will stop at 2.

(c) If hour hand of a clock starts from 10 and turns through 3 right angles, it will stop at 7.

(d) If hour hand of a clock starts from 7 and turns through 2 straight angles, it will stop at 7.