Courses
Courses for Kids
Free study material
Offline Centres
More
Store

A particle starts from the point (0, 8m) and moves with uniform velocity of m/s. After 2 seconds, the angular speed of the particle about the origin will beA) \eqalign{ & \dfrac{3}{{10}}rad/s \cr & \cr} B) \eqalign{ & \dfrac{6}{{25}}rad/s \cr & \cr} C) $\dfrac{{12}}{{25}}rad/s$ D) $\dfrac{3}{{50}}rad/s$

Last updated date: 19th Jun 2024
Total views: 385.8k
Views today: 4.85k
Verified
385.8k+ views
Hint: Apply distance formula for this question, we have to calculate the distance of the particle after traveling 2 seconds. With this value we create a new position of the particle, for this position we have to apply a distance formula to find the distance of this new position to the origin. After this we calculate angular velocity.

Complete Step by step solution:
To calculate the distance of the particle after traveling for 2 seconds. We consider the particle starts from (0, 8) m from rest with a uniform velocity of 3m/s in the x-direction so after 2 seconds the distance a particle will traverse along the x-axis is $3 \times 2 = 6m$.
So we get the new position of the particle is (6m, 8m).

Hence, the distance of this new position to the origin is =$\sqrt {{{\left( {x - 0} \right)}^2} + {{\left( {y - 0} \right)}^2}}$
\eqalign{ & \Rightarrow \sqrt {{{\left( {6 - 0} \right)}^2} + {{\left( {8 - 0} \right)}^2}} \cr & \Rightarrow \sqrt {{6^2} + {8^2}} \cr & \Rightarrow \sqrt {36 + 64} \cr & \Rightarrow \sqrt {100} \cr & \therefore 10 \cr}

Calculate, Angular velocity about origin is given by
$\omega = \dfrac{v}{r}$
V is the velocity of the particle
r is the new distance of particle
$\omega$ is the angular velocity.
Substitute given values we get

$\therefore \omega = \dfrac{3}{{10}}$ rad/sec.