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Laws Of Motion

Question
CBSEENPH11020323
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A pulley of radius 2m is rotated about its axis by a force F = (20t - 5t2) Newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg-m2, the number of rotations made by the pulley before its direction of motion if reversed is

  • more than 3 but less than 6

  • more than 6 but less than 9

  • more than 9

  • less than

Solution

A.

more than 3 but less than 6

To reverse the direction
integral τdθ space equals 0 straight tau space equals space left parenthesis 20 space straight t minus 5 straight t squared right parenthesis 2 space equals space 40 straight t minus 10 straight t squared straight alpha space equals space straight tau over straight I space equals space fraction numerator 40 straight t minus 10 straight t squared over denominator 10 end fraction space equals space 4 straight t minus straight t squared straight omega space equals space integral subscript 0 superscript straight t space αdt space equals space 2 straight t squared minus straight t cubed over 3 straight omega space is space zero space at 2 straight t squared minus straight t cubed over 3 space equals space 0 straight t cubed space equals space 6 straight t squared straight t space equals space 6 space sec straight theta space equals space integral ωdt space equals space integral subscript 0 superscript 6 left parenthesis 2 straight t squared minus straight t cubed over 3 right parenthesis dt open square brackets fraction numerator 2 straight t cubed over denominator 3 end fraction minus straight t to the power of 4 over 12 close square brackets subscript 0 superscript 6 space equals space 216 space open square brackets 2 over 3 minus 1 half close square brackets space equals space 36 space rad. No space of space revolution space fraction numerator 36 over denominator 2 straight pi end fraction space Less space than space 6

Some More Questions From Laws of Motion Chapter

Define inertia.

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

A person jumping out from a moving car or bus falls forward. Why?

Due to what type of inertia, the spark leaves the grind stone tangentially while sharpening the knife?

Which law of motion is also called law of inertia?

What is measure of inertia of body?

Which law of motion defines the force?

What happens to a stone tied to the end of string and whirled in a circle if the string suddenly breaks?

Which law of motion gives the quantitative knowledge of force?

Which law of motion is the real law of motion?

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