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Average velocity of tip of second hand of clock in an interval of 15s is ? (Length of second hand of clock is 15cm)

Average velocity of tip of second hand of clock in an interval of 15s is ? (Length of second hand of clock is 15cm)

Grade:11

2 Answers

Arun
25750 Points
6 years ago

Dear Rana

we know that

linear velocity (v) is related to angular velocity (ω) and radius vector (r) as

v = rω

here,

ω = θ/t

where  θ is the angular displacement covered in time 't'.

Now,

 

as the second hand moves 15 seconds

θ = π/2

t = 15 seconds

so,

ω = θ/t = π/2 / 15

or

ω = π/30 rad/sec

and thus, linear velocity of tip

v = rω

here,

r = 15cm = 0.15m

so,

v = 0.15 x π/30 m/sec

v = π/200 m/sec

 

Regards,

Arun (AskIITians Forum Expert)

Prashant Kumar
21 Points
6 years ago
Dear students (frnds)To find velocity First find the displacement of the second handTotal angle=360°In 60 sec --> 360°In 1 sec--> 6°15 sec--> 15*6= 90°Then using Pythagoras theoram find the hypotenuse i.e.,= displacement= 15√2cmV= dis./time= 15√2÷15= √2 cm/sThis is the correct ans The Sol. Is long here for better understanding but concept is easy

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