Question

In the given figure, a = 15 m/s² represents the total acceleration of a particle moving in the clockwise direction on a circle of radius R = 2.5 m at a given instant of time. The speed of the particle is ______.

पर्याय

• 6.2 m/s

• 4.5 m/s

• 5.0 m/s

• 5.7 m/s

Answer 1

In the given figure, a = 15 m/s² represents the total acceleration of a particle moving in the clockwise direction on a circle of radius R = 2.5 m at a given instant of time. The speed of the particle is 5.7 m/s.

Explanation:

Tan θ = `("dV"//"dt")/("V"^2//"R")`

Tan 30° = `1/sqrt3=("dV"//"dt")/("V"^2//"R")`

dV = `1/sqrt3xx"V"^2/"R"`

a = 15 = `sqrt(("dV"/"dt")^2+("V"^2/"R")^2)`

15 = `sqrt(4/3("V"^2/"R")^2)`

15 = `2/sqrt3("V"^2/"R")`

= `2/sqrt3xx"V"^2/2.5` 

⇒ V² = `(15xxsqrt3xx2.5)/2`

= 32.476 = 5.7 m/s