Answer
Verified
443.4k+ views
Hint-In the clock, the second hand, minute hand and the hour hand are rotating in the angular velocity. Here, we have to consider only the second hand and the minute hand. The second hand and the minute hand meet every second in an hour. Angular velocity is defined as the amount of time taken for the angular displacement. The angular velocity changes with the angle in which the object resides at a time $t$.
Formula used:
\[\omega = \dfrac{{2\pi }}{T}\]
Where,
\[\omega \]=the angular velocity
\[T\]=Time
\[2\pi \]=angular displacement
Complete step by step answer:
(i) Let's consider the one of the minutes in an hour, the second hand and the minute hand meet. We know $3600$ seconds in an hour and the $60$ seconds in a minute.
(ii) Let \[{\omega _1}\] and \[{\omega _2}\] are the angular velocities of the second hand and the minute hand and \[{T_1}\], \[{T_2}\] are the time period of second hand and the minute hand.
\[{\omega _1} = \dfrac{{2\pi }}{{3600}}\]; \[{\omega _2} = \dfrac{{2\pi }}{{60}}\]
(iii) \[\omega \Rightarrow \]\[{\omega _2} - {\omega _1}\]
\[ \Rightarrow \dfrac{{2\pi }}{{60}} - \dfrac{{2\pi }}{{3600}}\]
\[\omega \Rightarrow \dfrac{{2\pi \left( {59} \right)}}{{3600}}\]
(iv)To find the time of the known angular velocity,
\[\omega = \dfrac{{2\pi }}{T} \Rightarrow \] \[T = \dfrac{{2\pi }}{\omega }\]
Applying the value of \[\omega \] in the above time equation,
\[T = \dfrac{{2\pi \times 3600}}{{59 \times 2\pi }}\]
Cancelling \[2\pi \], we get
\[T = \dfrac{{3600}}{{59}}s\]
Hence the correct option is D.
Additional information:
(i) The velocity is the amount of linear displacement travelled in a period of time $t$. And its unit is metre per second. The angular velocity is the total amount of angular displacement travelled in a period of time $t$. ‘Radians per second’ is the unit of the angular velocity.
Note: The second and the minute hand meet every $60$ seconds. We can also say that the minute hand and the second hand meet every minute. We found the answer approximately equal to $60$seconds. We find this time period by evaluating the angular velocity. This describes how fast an object is moving in an orbit.
Formula used:
\[\omega = \dfrac{{2\pi }}{T}\]
Where,
\[\omega \]=the angular velocity
\[T\]=Time
\[2\pi \]=angular displacement
Complete step by step answer:
(i) Let's consider the one of the minutes in an hour, the second hand and the minute hand meet. We know $3600$ seconds in an hour and the $60$ seconds in a minute.
(ii) Let \[{\omega _1}\] and \[{\omega _2}\] are the angular velocities of the second hand and the minute hand and \[{T_1}\], \[{T_2}\] are the time period of second hand and the minute hand.
\[{\omega _1} = \dfrac{{2\pi }}{{3600}}\]; \[{\omega _2} = \dfrac{{2\pi }}{{60}}\]
(iii) \[\omega \Rightarrow \]\[{\omega _2} - {\omega _1}\]
\[ \Rightarrow \dfrac{{2\pi }}{{60}} - \dfrac{{2\pi }}{{3600}}\]
\[\omega \Rightarrow \dfrac{{2\pi \left( {59} \right)}}{{3600}}\]
(iv)To find the time of the known angular velocity,
\[\omega = \dfrac{{2\pi }}{T} \Rightarrow \] \[T = \dfrac{{2\pi }}{\omega }\]
Applying the value of \[\omega \] in the above time equation,
\[T = \dfrac{{2\pi \times 3600}}{{59 \times 2\pi }}\]
Cancelling \[2\pi \], we get
\[T = \dfrac{{3600}}{{59}}s\]
Hence the correct option is D.
Additional information:
(i) The velocity is the amount of linear displacement travelled in a period of time $t$. And its unit is metre per second. The angular velocity is the total amount of angular displacement travelled in a period of time $t$. ‘Radians per second’ is the unit of the angular velocity.
Note: The second and the minute hand meet every $60$ seconds. We can also say that the minute hand and the second hand meet every minute. We found the answer approximately equal to $60$seconds. We find this time period by evaluating the angular velocity. This describes how fast an object is moving in an orbit.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Which are the Top 10 Largest Countries of the World?
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Difference Between Plant Cell and Animal Cell
Give 10 examples for herbs , shrubs , climbers , creepers
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
How do you graph the function fx 4x class 9 maths CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE