Consider a string with several rocks tied along its length at equally spaced intervals. You whirl the string overhead so that the rocks follow circular paths. Compared with a rock at the end of the string, a rock at the middle moves Group of answer choiceshalf as fast.twice as fast.triple as fastat the same linear speed.
Question
Consider a string with several rocks tied along its length at equally spaced intervals. You whirl the string overhead so that the rocks follow circular paths. Compared with a rock at the end of the string, a rock at the middle moves Group of answer choiceshalf as fast.twice as fast.triple as fastat the same linear speed.
Solution
The speed of a rock tied to a string and whirled in a circular path depends on its distance from the center of the circle. The further the rock is from the center, the faster it moves. This is because all the rocks complete a revolution in the same amount of time, but the rocks further from the center have a longer path to travel.
So, compared to a rock at the end of the string, a rock in the middle of the string moves at half the speed. This is because it is half as far from the center of the circle, and therefore has half the distance to travel in the same amount of time.
So, the correct answer is "half as fast".
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A, B, C, D, and E practice running at a stadium that has several tracks. Each one starts running from the same point Z. A runs around a path which is an equilateral triangle ZYX. B runs around a square path ZYWV. C runs on a regular pentagonal path ZYUTS. D runs on a regular hexagonal path ZYRQPO. E runs along the trapezium ZYPO and completes one round in 20 seconds. Among all the tracks, there is a common side ZY, having length 100 m. The ratio of speeds of B and C is 5 : 4 respectively whereas the ratio of the time taken by A and D to complete one round of their tracks is 3 : 4 respectively. E's speed is the same as B's speed whereas A's speed is half that of C's.Note: The athletes maintain the same speeds in any track.Q 113. If A, B and C start running in the same direction along a 300 m long circular track, then after how much time will they meet for the first time?a) 60 secondsb) 90 secondsc) 75 secondsd) 120 seconds
A, B, C, D, and E practice running at a stadium that has several tracks. Each one starts running from the same point Z. A runs around a path which is an equilateral triangle ZYX. B runs around a square path ZYWV. C runs on a regular pentagonal path ZYUTS. D runs on a regular hexagonal path ZYRQPO. E runs along the trapezium ZYPO and completes one round in 20 seconds. Among all the tracks, there is a common side ZY, having length 100 m. The ratio of speeds of B and C is 5 : 4 respectively whereas the ratio of the time taken by A and D to complete one round of their tracks is 3 : 4 respectively. E's speed is the same as B's speed whereas A's speed is half that of C's.Note: The athletes maintain the same speeds in any track.Q 110. If E runs along the paths taken by A and B, then the time taken by him to complete 1 round each of the paths is approximately what percentage more or less than the total time taken by A and B?a) 46.24 % less timeb) 35.03 % more timec) 39.13 % less timed) 24.46 % less time
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