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Laws Of Motion

Question
CBSEENPH11020573

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

Solution

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