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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)
Dear Ranawe know thatlinear velocity (v) is related to angular velocity (ω) and radius vector (r) asv = rωhere,ω = θ/twhere θ is the angular displacement covered in time 't'.Now, as the second hand moves 15 secondsθ = π/2t = 15 secondsso,ω = θ/t = π/2 / 15orω = π/30 rad/secand thus, linear velocity of tipv = rωhere,r = 15cm = 0.15mso,v = 0.15 x π/30 m/secv = π/200 m/sec Regards,Arun (AskIITians Forum Expert)
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
r = 15cm = 0.15m
v = 0.15 x π/30 m/sec
v = π/200 m/sec
Regards,
Arun (AskIITians Forum Expert)
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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