Answer
Verified
36.3k+ views
Hint: We first need to calculate the angular displacement of the second hand of the clock in 1s. then we will use this to find the angular velocity of the clock. As we know that the linear velocity is the cross product of the radius of the circle and its angular velocity, so we can find linear velocity from this relation.
Complete step by step solution:
The angular velocity of a body is given as the angular displacement per unit time. a second-hand takes the 60s to complete 1 circle around the clock. This 1 one complete circle is represented as $2\pi $ . So the angular velocity of the tip of the clock will be:
$\omega = \dfrac{{2\pi }}{{60}} = \dfrac{\pi }{{30}} = \dfrac{{3.14}}{{60}} = 0.104$
Now, we know the angular velocity of the body. To find the linear velocity, we use:
$v = rx\omega $
$ \Rightarrow v = r\omega \sin \theta $
$ \Rightarrow v = 0.03 \times 0.104\sin (90)$
$ \Rightarrow v = 0.031$
Therefore, the option with the correct answer is option D. 0.104 $\dfrac{{rad}}{s}$ , 0.0031 $\dfrac{m}{s}$
Note:
In a uniform circular motion, the angular velocity does not change its magnitude because it is dependent on the angular displacement of the body. However, the linear velocity is dependent on the radius of the body and every point which lies on the radius of the circle will have a different angular velocity.
Complete step by step solution:
The angular velocity of a body is given as the angular displacement per unit time. a second-hand takes the 60s to complete 1 circle around the clock. This 1 one complete circle is represented as $2\pi $ . So the angular velocity of the tip of the clock will be:
$\omega = \dfrac{{2\pi }}{{60}} = \dfrac{\pi }{{30}} = \dfrac{{3.14}}{{60}} = 0.104$
Now, we know the angular velocity of the body. To find the linear velocity, we use:
$v = rx\omega $
$ \Rightarrow v = r\omega \sin \theta $
$ \Rightarrow v = 0.03 \times 0.104\sin (90)$
$ \Rightarrow v = 0.031$
Therefore, the option with the correct answer is option D. 0.104 $\dfrac{{rad}}{s}$ , 0.0031 $\dfrac{m}{s}$
Note:
In a uniform circular motion, the angular velocity does not change its magnitude because it is dependent on the angular displacement of the body. However, the linear velocity is dependent on the radius of the body and every point which lies on the radius of the circle will have a different angular velocity.
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
A hollow sphere of mass M and radius R is rotating class 1 physics JEE_Main
If the beams of electrons and protons move parallel class 1 physics JEE_Main
Two radioactive nuclei P and Q in a given sample decay class 1 physics JEE_Main
If a wire of resistance R is stretched to double of class 12 physics JEE_Main
Other Pages
when an object Is placed at a distance of 60 cm from class 12 physics JEE_Main
Sodium acetate on heating with soda lime produce A class 12 chemistry JEE_Main
Electric field due to uniformly charged sphere class 12 physics JEE_Main
Differentiate between homogeneous and heterogeneous class 12 chemistry JEE_Main
An electric bulb has a power of 500W Express it in class 11 physics JEE_Main
The nitride ion in lithium nitride is composed of A class 11 chemistry JEE_Main