Question

Two blocks having same mass are placed on rough incline plane as shown and the coefficient of friction between A and incline is ${\mu }_1=1.0$ and between block B and incline is ${\mu }_2=\frac{1}{\sqrt{3}}.$ As the inclination of the plane with respect to horizontal increases. Choose the correct answers(s).

• A. there is no contact force between block A and B as $\theta \le {30}^{\circ }$
• B. there is no contact force between blocks A and B as $\theta \le {45}^{\circ }$
• C. as ${\mu }_1>{\mu }_2$ both the blocks move together
• D. they starts moving at an angle $\theta =ta{n}^{-1}\left(\frac{{\mu }_1+{\mu }_2}{2}\right)$

Answer 1

Answer: (A), (C), (D)

The correct options are
A there is no contact force between block A and B as $\theta \le {30}^{\circ }$
C as ${\mu }_1>{\mu }_2$ both the blocks move together
D they starts moving at an angle $\theta =ta{n}^{-1}\left(\frac{{\mu }_1+{\mu }_2}{2}\right)$

As ${\theta }_1=ta{n}^{-1}\left({\mu }_1\right)and{\theta }_2=ta{n}^{-1}\left({\mu }_2\right)={45}^{\circ }={30}^{\circ }$

$\therefore If\theta <{30}^{\circ },thereisnocontactforcebetweenthem.$

For motion to start $2mgsin\theta =({\mu }_1+{\mu }_2)mgcos\theta$

$\therefore tan\theta =\frac{{\mu }_1+{\mu }_2}{2}$