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 :

Question

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 : (A)  tan θ (B)  2 tan θ (C)  3 tan θ (D)  tan 2 θ

Tardigrade Admin · Accepted Answer

Free body diagram is shown in the figure.
Psuedo force on the object is

2 m g

in the downward direction as seen from the rocket frame of reference.
Normal force in the direction perpendicular to the inclined plane.

N = 3 m g cos (θ) < b r / >

Maximum frictional force in the direction along the plane,

F_{r} = μ_{m} N

∴ F_{r} = 3 μ_{m} m g cos (θ)

This should balance the force on the block along the downward direction of plane.

3 m g sin (θ) = 3 μ_{m} m g cos (θ)

μ_{m} = tan (θ)

$tan θ$

$2 tan θ$

$3 tan θ$

$tan 2 θ$

tanθ

2tanθ

3tanθ

tan2θ

$tan θ$

$2 tan θ$

$3 tan θ$

$tan 2 θ$