Question

A block $X$ kept on an inclined surface just begins to slide, if the inclination is ${\theta }_1$. The block is replaced by another block $Y$ and it is found that it just begins to slide, if the inclination ${\theta }_2$ if ( ${\theta }_2>{\theta }_1$). Then

• A. Mass of X = mass of Y
• B. Mass of X < mass of Y
• C. Mass of X > mass of Y
• D. All the above three options are possible

Answer 1

Answer: (D)

All the above three options are possible

It is just about to slide .

So for X, we have $m_{x}gsin{\theta }_1=f_x$

For Y, we have $m_{y}gsin{\theta }_2=f_y$

now in case just to slide, $m_{x}gsin\theta ={\mu }_{sx}{m}_{x}cos\theta$

hence $\theta$ is independent of mass.

All three above mention cases are possible depending on the value of coefficient of friction.