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
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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
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