An insect is moving upwards on an inclined plane of inclination $θ$ . Between the inclined plane and the insect, coefficients of static and kinetic friction are $μ_{s}$ and $μ_{k}$ respectively $(μ_{s} > μ_{k}) .$ With what maximum acceleration can the insect move?

g s i n θ + μ_{s} g c o s θ

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g s i n θ + μ_{k} g c o s θ

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g s i n θ - μ_{k} g c o s θ

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μ_{s} g c o s θ - g s i n θ

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Solution

The correct option is B $g s i n θ + μ_{s} g c o s θ$
The maximum force required to move on an inclined plane with an acceleration a is the force required to overcome the sum of its weight and static friction force acting on
Thus
Static friction force is $f = μ_{s} N$
Weight component $m g s i n θ$
Force required
$F = m g s i n θ + μ_{s} m g c o s θ$
thus acceleration is
$a = \frac{F}{m}$
$a = g s i n θ + μ_{s} g c o s θ$
Option A is correct.

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An insect is moving upwards on an inclined plane of inclination θ. Between the inclined plane and the insect, coefficients of static and kinetic friction are μs and μk respectively (μs>μk). With what maximum acceleration can the insect move?

An insect is moving upwards on an inclined plane of inclination $θ$ . Between the inclined plane and the insect, coefficients of static and kinetic friction are $μ_{s}$ and $μ_{k}$ respectively $(μ_{s} > μ_{k}) .$ With what maximum acceleration can the insect move?