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How much angular distance will be covered by the minute hand of a correct clock in a period of 2 hours 20 minutes ?
520°
840°
320°
140°
None of the above
840°
The minute hand moves 360 degrees in 60 minutes, which is 6 degrees per minute. Simply multiply the total time in minutes by 6.
The minute hand moves 360 degrees in 60 minutes, which is 6 degrees per minute. Simply multiply the total time in minutes by 6.
Convert total time into minutes
2 hours = 2 multiplied by 60 = 120 minutes. Total time = 120 minutes + 20 minutes = 140 minutes.
Calculate angular velocity
The minute hand completes a full circle of 360 degrees in 60 minutes. Therefore, speed = 360/60 = 6 degrees per minute.
Calculate total angular distance
Total distance = 140 minutes multiplied by 6 degrees per minute = 840 degrees.
A: 520 degrees is incorrect as it results from miscalculating the minute conversion; C: 320 degrees is incorrect as it significantly underestimates the movement; D: 140 degrees is a common distractor representing only the total minutes without applying the 6 degrees per minute multiplier.
B is correct because the minute hand moves at a rate of 6 degrees per minute, and 140 minutes of movement equates to 140 multiplied by 6, which is 840 degrees.
Always convert the entire time duration into a single unit (minutes) first before applying rotational speed constants to avoid calculation errors.
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