Answer
Verified
44.4k+ 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
To get a maximum current in an external resistance class 1 physics JEE_Main
f a body travels with constant acceleration which of class 1 physics JEE_Main
If the beams of electrons and protons move parallel class 1 physics JEE_Main
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
Other Pages
when an object Is placed at a distance of 60 cm from class 12 physics JEE_Main
Electric field due to uniformly charged sphere class 12 physics JEE_Main
Formula for number of images formed by two plane mirrors class 12 physics JEE_Main
Differentiate between homogeneous and heterogeneous class 12 chemistry JEE_Main