Question

A wedge of mass M makes an angle $\theta$ with the horizontal. The wedge is placed on horizontal friction surface. A small block of mass m is placed on the inclined surface of wedge. What horizontal force F must be applied to the wedge so that the force of friction between the block and wedge is zero.

• A. Mg sin $\theta$
• B. Mg cos $\theta$
• C. Mg tan $\theta$
• D. 4Mg cot $\theta$

Answer 1

The correct option is D 4Mg cot $\theta$

$F=ma$

$m=\frac{F}{a}$

$f_p=ma$

$f_{p}sin\theta \ge 4macos\theta$

$\frac{F}{4m}sin\theta \ge gcos\theta$

$F\ge 4mgcot\theta$

$F_{min}=4mgcot\theta$