Answer
Verified
40.8k+ views
Hint: At first calculate how much the hour hand moves per hour and per minute.
Then calculate how much the minute hand moves per minute. Then find out the difference between them.
Complete step-by-step answer:
A clock is a circle. A circle always contains 360 degrees. A clock is divided up into 12 sectors, based on the numbers 1 to 12.
The hour hand of a clock moves 360 degrees in 12 hours.
So in one hour it will move $\dfrac{360}{12}=30$ degrees.
Again we can say that the hour hand moves 30 degrees in 1 hour or 60 minutes.
In 60 minutes it can move 30 degrees.
In one minute it can move $\dfrac{30}{60}=\dfrac{1}{2}={{0.5}^{\circ }}$
Now the minute hand of the clock completes a circle in one hour or we can say 60 minutes.
Therefore, in 60 minutes the minute hand moves 360 degrees.
So in one minute the minute hand can move $\dfrac{360}{60}=6$ degrees.
Now, the given time is 4.25 AM.
In 4 hour the hour hand will move $30\times 4=120$ degrees.
In 25 minutes the hour hand will move $0.5\times 25=12.5$ degrees.
So the hour hand will move $120+12.5=132.5$ degrees in total.
In 25 minute the minute hand will move $25\times 6=150$ degrees.
So the difference between the angle of the minute hand and the hour hand is:
${{\left( 150-132.5 \right)}^{\circ }}={{17.5}^{\circ }}$
$17.5=17\dfrac{5}{10}=17\dfrac{1}{2}$
Therefore the angle between the hands of a clock when the time is 4.25 AM is $17{{\dfrac{1}{2}}^{\circ }}$.
Hence, option (a) is correct.
Note: We generally make mistakes while calculating the movement of the hour hand. Generally we forget to add the minute part. Like here the time is 4.25 AM. That means the hour hand moves for 4 hours and 25 minutes. We have to calculate how much the hour hand moves in 25 minutes separately.
Then calculate how much the minute hand moves per minute. Then find out the difference between them.
Complete step-by-step answer:
A clock is a circle. A circle always contains 360 degrees. A clock is divided up into 12 sectors, based on the numbers 1 to 12.
The hour hand of a clock moves 360 degrees in 12 hours.
So in one hour it will move $\dfrac{360}{12}=30$ degrees.
Again we can say that the hour hand moves 30 degrees in 1 hour or 60 minutes.
In 60 minutes it can move 30 degrees.
In one minute it can move $\dfrac{30}{60}=\dfrac{1}{2}={{0.5}^{\circ }}$
Now the minute hand of the clock completes a circle in one hour or we can say 60 minutes.
Therefore, in 60 minutes the minute hand moves 360 degrees.
So in one minute the minute hand can move $\dfrac{360}{60}=6$ degrees.
Now, the given time is 4.25 AM.
In 4 hour the hour hand will move $30\times 4=120$ degrees.
In 25 minutes the hour hand will move $0.5\times 25=12.5$ degrees.
So the hour hand will move $120+12.5=132.5$ degrees in total.
In 25 minute the minute hand will move $25\times 6=150$ degrees.
So the difference between the angle of the minute hand and the hour hand is:
${{\left( 150-132.5 \right)}^{\circ }}={{17.5}^{\circ }}$
$17.5=17\dfrac{5}{10}=17\dfrac{1}{2}$
Therefore the angle between the hands of a clock when the time is 4.25 AM is $17{{\dfrac{1}{2}}^{\circ }}$.
Hence, option (a) is correct.
Note: We generally make mistakes while calculating the movement of the hour hand. Generally we forget to add the minute part. Like here the time is 4.25 AM. That means the hour hand moves for 4 hours and 25 minutes. We have to calculate how much the hour hand moves in 25 minutes separately.
Recently Updated Pages
Let gx 1 + x x and fx left beginarray20c 1x 0 0x 0 class 12 maths JEE_Main
The number of ways in which 5 boys and 3 girls can-class-12-maths-JEE_Main
Find dfracddxleft left sin x rightlog x right A left class 12 maths JEE_Main
Distance of the point x1y1z1from the line fracx x2l class 12 maths JEE_Main
In a box containing 100 eggs 10 eggs are rotten What class 12 maths JEE_Main
dfracddxex + 3log x A ex cdot x2x + 3 B ex cdot xx class 12 maths JEE_Main
Other Pages
when an object Is placed at a distance of 60 cm from class 12 physics JEE_Main
Write dimension of force density velocity work pre class 11 physics JEE_Main
Amongst LiCl RbCl BeCl2 and MgCl2the compounds with class 11 chemistry JEE_Main
Which of the following figures represent the variation class 12 physics JEE_Main
Excluding stoppages the speed of a bus is 54 kmph and class 11 maths JEE_Main
In an electromagnetic wave A Power is equally transferred class 12 physics JEE_Main