Question

A centripetal acceleration of 2.5 ms acts on a mass of 10 kg which forces the mass to execute uniform
circular motion. The radius of the circle is 10 m. then speed with which the mass travels is [ 1
a) 5 ms-
b) 6 ms-
c) 7 ms
d) 8 ms
A et plan is traveling a constant speed of insnlmnh Thamdin fl- 1.. .​

Answer 1

Given :

• Mass = 10 kg
• Centripetal acceleration (a) = 2.5 m/s²
• Radius (r) = 10m

To find :

• Velocity (v) with which the mass travels

Solution :

• We know that, centripetal acceleration is given by,

        a = ω² × r       where ω is the angular velocity

• Also, angular velocity is given by,

       ω = v ÷ r

• ∴  $a = \frac{v^{2} }{r}$  

        ∴ v² = a × r

                 = 2.5 × 10

        ∴  v² = 25

        ∴  $v = \sqrt{25}$  

        ∴ v = 5 m/s

Answer : The speed with which the mass travels is 5 m/s. Hence option  (a) is the right answer.

Answer 2

m = 10 kg

a= 2.5 m/s

r= 10 m

a= w square×r

a= v square/ r

v square= a×r = 2.5 ×10

v square = 25 = √ 25

v= 5 m/s

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