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Laws of Motion

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Physics Part I

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Physics

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The ratio of the accelerations for a solid sphere (mass m and radius R) rolling down an incline of angle straight theta without slipping and slipping down the incline without rolling is,

  • 5:7

  • 2:3

  • 2:5

  • 7:5


A.

5:7

A solid sphere rolling without slipping down an inclined plane is,

We have in this case,

a subscript 1 space equals space fraction numerator straight g space sin space straight theta over denominator 1 plus space begin display style straight k squared over straight R squared end style end fraction space equals space fraction numerator g space sin space theta over denominator 1 space plus open parentheses space begin display style bevelled 2 over 5 end style close parentheses end fraction
F o r space s o l i d space s p h e r e comma space K squared space equals space 2 over 5 R squared
space space space space space space equals space fraction numerator g space sin space theta over denominator begin display style bevelled 7 over 5 end style end fraction
rightwards double arrow space a subscript 1 space equals space 5 over 7 space g space sin space theta
For a sphere slipping down an inclined plane,

straight a subscript 2 space equals space straight g space sin space straight theta

That space is comma

space space space space space space straight a subscript 1 over straight a subscript 2 space equals space fraction numerator bevelled 5 over 7 space straight g space sin space straight theta over denominator straight g space sin space straight theta end fraction
rightwards double arrow space straight a subscript 1 over straight a subscript 2 space equals space 5 over 7

A solid sphere rolling without slipping down an inclined plane is,

We have in this case,

a subscript 1 space equals space fraction numerator straight g space sin space straight theta over denominator 1 plus space begin display style straight k squared over straight R squared end style end fraction space equals space fraction numerator g space sin space theta over denominator 1 space plus open parentheses space begin display style bevelled 2 over 5 end style close parentheses end fraction
F o r space s o l i d space s p h e r e comma space K squared space equals space 2 over 5 R squared
space space space space space space equals space fraction numerator g space sin space theta over denominator begin display style bevelled 7 over 5 end style end fraction
rightwards double arrow space a subscript 1 space equals space 5 over 7 space g space sin space theta
For a sphere slipping down an inclined plane,

straight a subscript 2 space equals space straight g space sin space straight theta

That space is comma

space space space space space space straight a subscript 1 over straight a subscript 2 space equals space fraction numerator bevelled 5 over 7 space straight g space sin space straight theta over denominator straight g space sin space straight theta end fraction
rightwards double arrow space straight a subscript 1 over straight a subscript 2 space equals space 5 over 7
2280 Views

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. 
1475 Views

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.
2445 Views

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. 
1332 Views

Is Aristotle’s law of motion now correct?

No. Aristotl'e law of motion is false. 
1233 Views

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. 
1316 Views