Question

(i) A cyclist goes around a circular track once in every 2 minutes, with
uniform speed. If the radius of the circular track is 210m, calculate his speed (∏ = 22/7).
(ii) Will the cyclist go round the track with acceleration?

Answer 1

Answer:

44

Explanation:

first find the circumference

2 22/7 210

44 30

1320 m = Distance

Speed =Distance Time

=1320 2/60 (Converting 2 min into sec by 60)

=44

Answer 2

Answer:

Centripetal Acceleration, Ac= 0.57 m/s²

Explanation:

Since, the speed is uniform, it is a case of uniform circular motion. Now;-

(i) Given;-

            Time, t= 2 min

                       = 120 seconds

            n = 1 [where = number of rounds]

Since;-

            Ac= V²/R = ω² × R  [where Ac is centripetal acceleration and others are formula units of Ac]

So,

            Ac= ω² × R   _____(1)

Since, ω = θ/ t

           ω = 2π × n/ t

           ω = 2π × 1/ 120

           ω = π/ 60 _____(2)

Putting (2) in (1), we obtain;-

           Ac= (π/ 60)² × 210

           Ac= (22 × 22 / 7 × 7 × 60 × 60) × 210

           Ac= 101640/ 176400

           Ac= 0.57 m/s² ( approx )

(ii) Yes, the cyclist would round the the track with centripetal acceleration [Refer to attached image to understand this]

Hope it helps! ;-))