Question

❤❤❤Hey❤❤❤
What do you mean by uniform circular motion? Derive an expression for acceleration of an object in uniform circular motion.
A stone tied to the end of a string 0.8 m long is whirled in a horizontal circle with a constant speed.
If the stone makes 14 revolutions in 25 seconds, what is the acceleration of the
stone?
Carries 5 Marks

Class 11 CBSE

Answer 1

Answer:

(A) When a body revolves in a circular path, such that it's speed is constant, it is called uniform circular motion. Though the speed is constant, the velocity changes continously due to change in direction of the body at every point. This change in velocity is caused by the centripetal acceleration, which in turn is caused by centripetal force. This centripetal acceleration is given as V^2/R, where v = speed of the body.

(B) Given,

radius of the circle = 0.8 m

The stone makes 14 revolutions in 25 seconds.

Therefore,

omega = (14 × 2 pi rad)/25s = 28 pi rad/25 s. = 3.51 rad/s

We know,

v = r × omega = 0.8 × 3.51 = 2.8 m/s

Now, Acceleration = v^2/R = (2.8)^2/(0.8)

so, Acceleration = 7.84/0.8 = 9.8 m/s^2