A particle is moving along a circular path with a constant speed of 10 ms-1. What is the magnitude of the change is velocity of the particle, when it moves through an angle of 60° around the centre of the circle?

Question

A particle is moving along a circular path with a constant speed of 10 ms-1. What is the magnitude of the change is velocity of the particle, when it moves through an angle of 60° around the centre of the circle? (A) zero (B) 10 m/s (C) 10 √3 m/s (D) 10 √2 m/s

Tardigrade Admin · Accepted Answer

Q. A particle is moving along a circular path with a constant speed of $10 m s^{- 1}$ . What is the magnitude of the change is velocity of the particle, when it moves through an angle of $6 0^{\circ}$ around the centre of the circle?

$zero$

$10 m / s$

$103 m / s$

$102 m / s$

$∣ Δ \overset{v}{ˉ} ∣ = v_{1}^{2} + v_{2}^{2} + 2 v_{1} v_{2} cos (π - θ)$
$= 2 v sin \frac{θ}{2} since [∣ \overset{v_{1}}{ˉ} ∣ = ∣ \overset{v_{2}}{ˉ} ∣]$
$= (2 \times 10) \times sin (3 0^{\circ})$
$= 10 m / s$

Q. A particle is moving along a circular path with a constant speed of 10ms−1. What is the magnitude of the change is velocity of the particle, when it moves through an angle of 60∘ around the centre of the circle?

zero

10m/s

103​m/s

102​m/s