A spherical solid ball rolls on a table. What fraction of its total kinetic energy is rotational kinetic energy?

Solution

When a body rolls without slipping, it possesses both rotational kinetic energy and translational kinetic energy.
Total kinetic energy of solid ball is,
K.E = K_t + K_r
$straight K. straight E space equals space 1 half space Iω squared space plus space 1 half mv squared space space space space space space space space equals 1 half open parentheses 2 over 5 MR squared close parentheses straight omega squared space plus space 1 half mv squared space space space space space space equals space 1 fifth MR squared space straight omega squared space plus space 1 half mv squared space space space space space space space equals space 1 fifth mv squared space plus space 1 half mv squared space straight K. straight E space equals space 7 over 10 space mv squared That space is comma space Rotational space straight K. straight E space equals space 1 fifth mv squared space So comma space Total space straight K. straight E space equals space 7 over 10 space mv squared space Fractional space rotational space straight K. straight E space equals space bevelled fraction numerator begin display style 1 fifth end style mv squared over denominator 7 over 10 space mv squared space end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 2 over 7$

Some More Questions From Units and Measurement Chapter

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Units And Measurement

A spherical solid ball rolls on a table. What fraction of its total kinetic energy is rotational kinetic energy?

Some More Questions From Units and Measurement Chapter

Give four examples of physical quantities.

Define unit.

What are the two main required characteristics of a unit?

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.

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