-->

Laws Of Motion

Question
CBSEENPH11020605

The upper half of an inclined plane of the inclination straight theta is perfectly smooth while lower half is rough. A block starting from rest at the top of the plane will again come to rest at the bottom, if the coefficient of friction between the block and lower half of the plane is given by,

  • straight mu space equals space fraction numerator 1 over denominator tan space straight theta end fraction
  • straight mu space equals space fraction numerator 2 over denominator tan space straight theta end fraction
  • straight mu space equals space 2 space tan space straight theta
  • straight mu space equals space tan space straight theta

Solution

C.

straight mu space equals space 2 space tan space straight theta
The block will be stationary when,

mg sin straight theta . L = straight alpha mg cos straight theta space. space straight L over 2
straight mu space equals space fraction numerator mg space sin space straight theta space straight L over denominator mg space cos space straight theta space begin display style bevelled straight L over 2 end style space end fraction

space space equals space 2 space fraction numerator sin space straight theta over denominator cos space straight theta end fraction

space space equals space 2 space tan space straight theta

straight mu equals space 2 space tan space straight theta