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Laws of Motion

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Physics Part I

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Class 10 Class 12

A stone of mass 0.25 kg tied to the end of a string is whirled round in a circle of radius 1.5 m with a speed of 40 rev./min in a horizontal plane. What is the tension in the string? What is the maximum speed with which the stone can be whirled around if the string can withstand a maximum tension of 200 N?

We have, 

Mass of the stone, m = 0.25 kg

Radius of the circle, r = 1.5 m

Number of revolution per second, n =

40 over 60 equals space 2 over 3 space r. p. s 40 / 60 = 2 / 3 rps
Angular velocity, ω = straight v over straight r = 2πn 

The tension in the string provides the centripetal force. 


T = Fcentripetal 

   = mv squared over straight r 

    = mrω

    = mr(2πn)

    = 0.25 × 1.5 × (2 × 3.14 × (open parentheses 2 over 3 close parentheses)2
    = 6.57 N 

Maximum tension in the string,

         Tmax = 200 N 

           max = mv2max / r

∴       vmax = (Tmax × r  / m)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. 

Is Aristotle’s law of motion now correct?

No. Aristotl'e law of motion is false. 

What is Aristotle’s law of motion?

Aristotle’s law of motion states that an external force is required to keep the body in motion.

Define inertia.

The property by virtue of which the body cannot change its state of rest or uniform motion in a straight line, unless an external force is acting on the body is called as Inertia. 

When the branches of an apple tree are shaken, the apples fall down. Why?

The apple fall from an apple tree when it shaken because of inertia of rest. Apple is in a state of rest and when the tree is suddenly shaken, apples still tends to remain in it's same state of rest whereas branches move. 

So, the apples fall down. 

State Galileo’s law of motion.

Galileo’s law of motion states that, a body continues to move in the same direction with constant speed, if no force is acting on the body.