if a stone a mass 0.25 kg tied to a string executes unoform motion with a speed of 2ms-¹of radius 3m, what is magnatitude of tensional force acting on the stone?
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Answer:
Mass of the stone, m=0.25 kg
Radius of the circle, r=1.5 m
Number of revolution per second, n=40/60=2/3rps
Angular velocity, ω=2πn
The centripetal force for the stone is provided by the tension T, in the string, i.e.,
T=mω
2
r
=0.25×1.5×(2×3.14×(2/3))
2
=6.57 N
Maximum tension in the string, T
max
=200 N
T
m
ax=
r
mv
max
2
v
max
=(
m
T
max
r
)
1/2
=(200× 1.5/0.25)
1/2
=(1200)
1/2
= 34.64 m/s
Therefore, the maximum speed of the stone is 34.64 m/s.
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