The second's hand of a watch has 6, cm length | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Given: length of the second's hand $l = 6\, cm = 60\, mm$.Time period $T = 60\, s$.Angular velocity $\omega = \frac{2\pi}{T} = \frac{2\pi}{60} = \

Vedclass · Accepted Answer

$2\pi$ and $2\sqrt{2}\pi\, mm/s$

Vedclass · Answer

(D) Given: length of the second's hand $l = 6\, cm = 60\, mm$.Time period $T = 60\, s$.Angular velocity $\omega = \frac{2\pi}{T} = \frac{2\pi}{60} = \frac{\pi}{30}\, rad/s$.Speed of the tip $v = \omega l = \frac{\pi}{30} 	imes 60\, mm/s = 2\pi\, mm/s$.At two perpendicular positions,the velocity vectors are $\vec{v}_1$ and $\vec{v}_2$,where $|\vec{v}_1| = |\vec{v}_2| = v$.The magnitude of the difference in velocities is $|\Delta \vec{v}| = |\vec{v}_1 - \vec{v}_2| = \sqrt{v^2 + v^2} = v\sqrt{2}$.Substituting $v = 2\pi\, mm/s$,we get $|\Delta \vec{v}| = 2\pi 	imes \sqrt{2} = 2\sqrt{2}\pi\, mm/s$.

The second's hand of a watch has $6\, cm$ length. The speed of its tip and the magnitude of the difference in velocities of its tip at any two perpendicular positions will be respectively:

Similar Questions

The relative angular speed of the hour hand and the minute hand of a clock is:

$A$ projectile can have the same range $(R)$ for two angles of projection. Their initial velocities are same. If $T_1$ and $T_2$ are times of flight in two cases,then the product of two times of flight is directly proportional to

$A$ spherical bob of mass $250 \ g$ is attached to the end of a string having length $50 \ cm$. The bob is rotated on a horizontal circular path about a vertical axis. The maximum tension that the string can bear is $72 \ N$. The maximum possible value of angular velocity of the bob (in $rad/s$) is

$A$ body is moving with velocity $30 \; m/s$ towards east. After $10 \; s$,its velocity becomes $40 \; m/s$ towards north. The average acceleration of the body is ...... $m/s^2$.

If two bodies $A$ and $B$ are projected with the same velocity $u$ but with different angles $\theta_1$ and $\theta_2$ respectively with the horizontal such that both have the same range,then the ratio of the times of flight of the bodies $A$ and $B$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module