
Where will the hand of a clock stop?
(a) starts at 12 and makes \[\dfrac{1}{2}\] of a revolution, clockwise?
(b) starts at 2 and makes \[\dfrac{1}{2}\] of a revolution, clockwise?
(c) starts at 5 and makes \[\dfrac{1}{2}\] of a revolution, clockwise?
(d) starts at 5 and makes \[\dfrac{3}{4}\] of a revolution, clockwise?
Answer
524.1k+ views
Hint: For solving this question you should know about the segments of a clock. As we know that the total number of segments in the clock is 12 and every segment is covered at the end of each hour. We will use this concept to solve this question. We will count the total hours in every segment and then divide it by total segments of a clock and find the next point by the given fraction if there is given that.
Complete step by step solution:
According to our question it is asked to us where the hand of a clock stops if it continues at given points.
So, as we know, the total number of segments in a clock is 12. And for counting the fractions of a clockwise segment we will use the total number of hours as 12. And then we calculate the difference between both the timings or so in 1 complete clockwise revolution, the hand of a clock will rotate by \[{{360}^{\circ }}\].
(a) When the hand of a clock starts at 12 and makes \[\dfrac{1}{2}\] of a revolution clockwise then it will rotate by \[{{180}^{\circ }}\], and hence it will stop at 6.
(b) When the hand of a clock starts at 2 and makes \[\dfrac{1}{2}\] of a revolution clockwise then it will rotate by \[{{180}^{\circ }}\], and hence it will stop at 8.
(c) When the hand of a clock starts at 5 and makes \[\dfrac{1}{2}\] of a revolution clockwise then it will rotate by 180 degrees, and hence it will stop at 11.
(d) When the hand of a clock starts at 5 and makes \[\dfrac{3}{4}\] of a revolution clockwise, then it will rotate by 270 degrees and hence it will stop at 2.
And we can calculate all these by just a simple formula:
Fractional revolution \[=\dfrac{\text{difference of hours}}{\text{Total no. of segments}}\]
Thus, the difference = fractional revolution \[\times \] Total no. of revolution
And then we increase our point by the determined point.
Note: While solving this question you should be careful of the total segments of that given and always find the difference of that points or hours and it will be counted through a given point from where it will start. And if the starting point is not given then start that from 00:00 or 12:00 in both the conditions the answer will be the same.
Complete step by step solution:
According to our question it is asked to us where the hand of a clock stops if it continues at given points.
So, as we know, the total number of segments in a clock is 12. And for counting the fractions of a clockwise segment we will use the total number of hours as 12. And then we calculate the difference between both the timings or so in 1 complete clockwise revolution, the hand of a clock will rotate by \[{{360}^{\circ }}\].
(a) When the hand of a clock starts at 12 and makes \[\dfrac{1}{2}\] of a revolution clockwise then it will rotate by \[{{180}^{\circ }}\], and hence it will stop at 6.
(b) When the hand of a clock starts at 2 and makes \[\dfrac{1}{2}\] of a revolution clockwise then it will rotate by \[{{180}^{\circ }}\], and hence it will stop at 8.
(c) When the hand of a clock starts at 5 and makes \[\dfrac{1}{2}\] of a revolution clockwise then it will rotate by 180 degrees, and hence it will stop at 11.
(d) When the hand of a clock starts at 5 and makes \[\dfrac{3}{4}\] of a revolution clockwise, then it will rotate by 270 degrees and hence it will stop at 2.
And we can calculate all these by just a simple formula:
Fractional revolution \[=\dfrac{\text{difference of hours}}{\text{Total no. of segments}}\]
Thus, the difference = fractional revolution \[\times \] Total no. of revolution
And then we increase our point by the determined point.
Note: While solving this question you should be careful of the total segments of that given and always find the difference of that points or hours and it will be counted through a given point from where it will start. And if the starting point is not given then start that from 00:00 or 12:00 in both the conditions the answer will be the same.
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