Question

If the coefficient of friction between A and B is $\mu$, the maximum acceleration of the wedge A for which B will remain at rest with respect to the wedge is

• A. $\mu g$
• B. $g\left(\frac{1+\mu }{1-\mu }\right)$
• C. $g\left(\frac{1-\mu }{1+\mu }\right)$
• D. $\frac{g}{\mu }$

Answer 1

Answer: (B)

$g\left(\frac{1+\mu }{1-\mu }\right)$

B experiences a pseudo acceleration towards the left in A's frame, call this '$a$'
Thus, for B to remain at rest,
$\mu (g\cos 45+a\sin 45)=a\cos 45-g\sin 45$
because normal reaction on B is $m(g\cos 45+a\sin 45)$
$g(\mu +1)=a(1-\mu )$
$a=\frac{g(\mu +1)}{(1-\mu )}$