A block A kept on an inclined surface just begins to slide if the inclination is $30^\circ$. The block is replaced by another block B and it is found that it just begins to slide if the inclination is $40^\circ$.

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KollegeApply · Accepted Answer

all of three are possible We know that N = mg cos $\theta$˚ fmax = μN = μmg cos $\theta$ where N = normal reaction force fmax = frictional force $\theta$ = angle of inclination μ = coefficient of friction When the block just begins to slide, it means mg sin $\theta$ = fmax mg sin $\theta$ = μmg cos $\theta$ μ = tan $\theta$ and the coefficient of friction depends on the angle of inclination ($\theta$) and does not depend on mass. Now consider the block sliding condition: mg sin $\theta$ − fmax = ma mg sin $\theta$ − μmg cos $\theta$ = ma $\therefore$ a = g(sin $\theta$ − μ cos $\theta$) From the above equation it is clear that acceleration does not depend on the mass but depends on $\theta$ and μ. [Solution diagram: 66592_solution_1.png]

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