Question

If a stone of mass of 2kg tied to a string executes uniform circular motion with a speed of 2ms-1 of radius 2m. What is the magnitude of tensional force acting on the stone?

Answer 1

Explanation:

Mass of stone(m) = 2Kg,

radius(r) = length of rope =2m,

Maximum tension (T max ) = 400N

The maximum tension acts as the centripetal force for the circular motion of the stone.

Let v

max be the maximum velocity.

Hence, F=T

max = rmv max2

⇒v max2 = mT max ×r

⇒v max = mT max ×r

⇒v max= 2400×2

⇒v max =20ms −1

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Answer 2

Answer:

Mass, m=0.2 kg

Radius, r=1 m

Angular speed, ω=90 rpm

⟹ω=

60

90

⟹ω=1.5 rps

⟹ω=3π rad/s

(a) Angular velocity, ω=3π rad/s

(b) Centripetal acceleration. a=rw

2

⟹a=1×3π×3π

⟹a=9π

2

m/s

2

(c) Centripetal Force, F=ma

⟹F=0.2×9π

2

⟹F=1.8π

2

N

(d) Tension in string, = Centripetal Force

⟹T=F=1.8π

2

N

Explanation:

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