Question

13. A dot makes a turn in a circle 5 times in a
second. The radius of the circle is 5 cm and
the dot moves uniformly, the acceleration
of the dot is (in SI units)
?
1)π^2/125. 2)2π^2. 3)zero. 4)5π^2
​

Answer 1

Explanation:

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Answer 2

Given info : A dot makes a turn in a circle 5 times in a second. The radius of the circle is 5 cm and the dot moves uniformly.

To find : the acceleration of the dot is ...

solution : centripetal acceleration is the rate of change of angular velocity with respect to time.

i.e., α = dω/dt

centripetal acceleration is also given as, α = ω²R

where R is radius of circular path.

angular velocity , ω = dθ/dt

a/c to question, The dot makes turn in a circle 5 times in a second.

so, θ = 2π × 5 = 10π

t = 1 s

so, ω = 10π rad/s

and radius, R = 5 cm = 5/100 = 1/20 m

now α = (10π rad/s)² × 1/20 m = 100π²/20 = 5π² m/s²

Therefore the acceleration of the dot is 5π² m/s². that is option (4) is correct.