Question

14. Minute hand of a clock is 10 cm long. Find
the average speed of its tip from 3.00 p.m. to
3.15 pm.
a)
107
cm/sec
900
b) cm/sec
900
c)
1012
cm/sec
900
d) None​

Answer 1

Solution :-

Here , the length of minute hand is 10cm , so the minute hand will be radius & here the minute hand moves from 3:00 pm - 3:15 pm , so as we know that the angle between 3:00pm - 3:15pm is 90° .

As we know that , length of arc = rθ [where θ is in radians] . Since θ is in degrees , we need to convert it into radians → 90° = 180°/2 = π/2 [180° = π]

→ length of arc = 10 × π/2

→ length of arc = 5π

And here the time between 3:00pm & 3:15pm is 15min , so here it is in mins , converting into seconds → 15mins = 900s

Now , speed = distance/time

=> Speed = 5π/900

=> Speed = π/180

=> Speed = 0.017 cm/s

Hence , speed of its tip = 0.017cm/s . So option d(none) is your answer .

Answer 2

${\large{\bold{\sf{\underline{Correct \: question}}}}}$

➨ Minute hand of a clock is 10 cm long. Find the average speed of its tip from 3.00 p.m. to 3:15 pm.

Options --

• 107 cm/sec
• 900 cm/sec
• 1012 cm/sec
• None

${\large{\bold{\sf{\underline{Understanding \: the \: question}}}}}$

➨ This question says that there is a minute hand clock of 10 cm in length. And we have to find the average speed of its tip from 3.00 p.m. to 3:15 pm. Means there are 15 minutes here (atq)

${\large{\bold{\sf{\underline{Given \: that}}}}}$

➨ Minute hand clock of 10 cm in length

${\large{\bold{\sf{\underline{To \: find}}}}}$

➨ The average speed of its tip from 3.00 p.m. to 3:15 pm

${\large{\bold{\sf{\underline{Solution}}}}}$

➨ The average speed of its tip from 3.00 p.m. to 3:15 pm = Option d None

${\large{\bold{\sf{\underline{Using \: concept}}}}}$

➨ Length of arc = r(radian)

➨ Speed = Distance / Time

${\large{\bold{\sf{\underline{Full \: solution}}}}}$

~ Let's convert radian into degrees as we already know that given time is 3:00 pm to 3:15 pm and these form an angle of 90° always! Henceforth,

➨ 90° = ${\bold{\sf{\dfrac{180}{2}}}}$°

➨ 90° = 90° but atq ${\bold{\sf{\dfrac{\pi}{2}}}}$°

☃ Finding length of arc

➨ 10 × ${\bold{\sf{\dfrac{\pi}{2}}}}$°

➨ 5π

~ Converting minutes into seconds

➨ Here, 15 minutes

➨ 1 minute = 60 seconds

➨ Hence, 15 × 60

➨ 900 seconds

☃ Now finding speed of it's tip

➨ Speed = Distance / Time

➨ Speed = ${\bold{\sf{\dfrac{5 \pi}{900}}}}$

➨ Speed = ${\bold{\sf{\dfrac{\pi}{180}}}}$

• Converting....

➨ Speed = 0.017 cm/s

• Henceforth, 0.017 cm/s is the average speed of its tip from 3.00 p.m. to 3.15 pm. Means the correct answer of this question is Option d ( none )