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Units And Measurement

Question
CBSEENPH11020676
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A small mass attached to a string rotats on frictionless table top as shown. If the tension is the string is increased by pulling the string causing the radius of the circular  motion to decrease by a factor of 2, the kinetic energy of the mass will

  • remain constant

  • increase by a factor of 2

  • increase by a factor 4 

  • decrease by a factor of 2

Solution

C.

increase by a factor 4 

From the law of conservation of angular momentum
mvr space equals space mv apostrophe straight r over 2 straight v apostrophe space equals space 2 straight v So comma space straight k subscript 1 over straight k subscript 2 space equals space fraction numerator begin display style 1 half end style mv squared over denominator begin display style 1 half end style mv apostrophe squared end fraction straight k subscript 1 over straight k subscript 2 space equals space fraction numerator straight v squared over denominator straight v apostrophe squared end fraction space equals space fraction numerator straight v squared over denominator left parenthesis 2 straight v right parenthesis squared end fraction straight k subscript 1 over straight k subscript 2 space equals space 1 fourth straight k subscript 1 space equals space 4 straight k subscript 1

Some More Questions From Units and Measurement Chapter

Can we use same units for different physical quantities?

Can we use different units to measure same physical quantity?

To measure a physical quantity X, the unit U is repeatedly used for n times. What is the magnitude of physical quantity?

Does the numerical factor in the quantitative measurement depend on the system of unit used?

Is one unit sufficient to measure a physical quantity?

Can a physical quantity have two or more units? Give example.

What are fundamental quantities?

How many fundamental quantities are there in mechanics?

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