Question

A body of mass 1 kg tied to one end of string is revolved in a horizontal circle of radius 0.1 m with a speed of 3 revolution/sec, assuming the effect of gravity is negligible, then linear velocity, acceleration and tension in the string will be nearly​

Answer 1

Solution :

As per the given data ,

• Mass of the body (m) = 1 kg
• Radius of the string (r) = 0.1 m
• Frequency (f) = 3 rev / s

(1) Linear velocity (v)

We know that ,

➜ ω = 2 π f

➜ ω = 2 π x 3

➜ ω = 6 π

➜ ω = 6 x 3.14

➜ ω = 18.84 rad /s

Linear velocity is given by ,

➜ v = ω r

➜ v = 18.84 x 0.1

➜ v = 1.884 m /s

The linear velocity of the body is 18.84 m/s .

(2) Acceleration (ac )

The body is moving in circular motion due to the centripetal acceleration acting on it ,

➜ a c = v ² / r

➜ a c = 1.884 x 1.884 / 0.1

➜ ac = 35.4 m/s²

The centripetal acceleration acting on the body is 35.4 m/s²

(3) Tension in the string ( F)

Centripetal force acting on the body is given by ,

➜ F = m v ² / r

➜ F = 1 x 35 . 4

➜ F = 35 .4 N

The tension acting on the string is 35.4 N