A uniform beam of mass m is
inclined at an angle `theta` to the
horizontal. Its upper end
produces a `90^(@)` bend in a very
rough rope tied to a wall, and
its lower end rests on a rough
floor(see figure). If the
coefficient of static friction
between the beam and the floor
is `mu` then the maximum value of
M is given by the expression

Options

A. `M le(m(2 mu-cot theta))/(2(cot theta-mu))`
B. `M le(mu m)/((1-3 mu))`
C. `M le(m(2mu-tan theta))/(2(tan theta-mu))`
D. `M le(m)/((1-3 mu))`

Answer

A

Explanation

If the net torque about the lowest
point is set equal to zero, we get,
Mg L cos `theta+ mg""(L)/(2)cos theta-mu N.Lsin theta=0`
Where N=(M+m)g.