By Team Aakash Byju's | 19th November 2022
A weightless thread can withstand tension up to 30 N. A stone of mass 0.5 kg is tied to it and is revolved in a circular path of radius 2 m in a vertical plane. If g = 10 ms, then
(Angular velocity)
-2
maximum
=
√30 rad/s
A.
(Angular velocity)
maximum
=
√60 rad/s
B.
(Angular velocity)
maximum
=
5 rad/s
C.
maximum
=
6 rad/s
D.
(Angular velocity)
For the given situation, when the stone is at the lowest position of the vertical motion, the tension is maximum.
W
T
r
Mass of the object and gravity
Radius
Angular velocity
Tension
mg
W
T
r
Mass of the object and gravity
Radius
Angular velocity
Tension
mg
Using the equation of circular motion we can write:
mr
( w )
max
2
=
T
max
-mg
Where, w is the maximum angular velocity.
max
W
T
r
Mass of the object and gravity
Radius
Angular velocity
Tension
mg
T = 30 N, m = 0.5 kg, r = 2 m, g = 10 ms
max
-2
(0.5)(2) (w ) = 30 − (0.5 × 10)
max
2
Given,
W
T
r
Mass of the object and gravity
Radius
Angular velocity
Tension
mg
=>(w ) =30 − 5 = 25
max
=>w = 5 radians per second.
max
2