A rocket is fired  vertically from the earth with an acceleration of 2g, where g is the gravitational acceleration.  On an inclined plane inside the rocket, making an angle θ with the horizontal, a point object of mass m is kept.  The minimum coefficient of friction µmin between the mass and the inclined surface such that the mass does not move is :

  • Option 1)

    tanθ

  • Option 2)

     2 tanθ

  • Option 3)

    3 tanθ

  • Option 4)

    tan2θ

 

Answers (1)

As we learnt in

Kinetic or Dynamic Friction -

f_{K}\;\alpha\ R

f_{K}=\mu_{K} R

f_{K}= kinetic friction 

\mu_{K}= coefficient of kinetic friction

R = reaction

- wherein

f_{K}<F_{l}

\therefore\ \mu_{K}<\mu_{s}

\mu_{K}=depends on the nature of surface in contact.

 

 Since the rocket is moving vertically upwards with acceleration 2g therfore the apparent acceleration experienced by the point object is g + 2g = 3g 

Vertically downwards

Where N = 3 mg\ cos \theta

3 mg\ sin\theta=\mu\ 3 mg\ cos\theta

\mu=tan\theta

Correct option is 1.

 


Option 1)

tanθ

This is the correct option.

Option 2)

 2 tanθ

This is an incorrect option.

Option 3)

3 tanθ

This is an incorrect option.

Option 4)

tan2θ

This is an incorrect option.

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