Question

A block of mass m is placed on a smooth inclined wedge ABC of inclination $\theta$ as shown in the figure. The wedge is given an acceleration 'a' towards the right. The relation between a and $\theta$ for the block to remain stationary on the wedge is

• A. $\text{a = g cos}\theta$
• B. $a=\frac{g}{\text{sin}\theta }$
• C. $a=\frac{g}{\text{cosec}\theta }$
• D. $\text{a = g tan}\theta$

Answer 1

The correct option is D $\text{a = g tan}\theta$


In non - inertial frame,
$\text{N sin}\theta =\text{ma .........(i)}$
$\text{N cos}\theta =\text{mg ..........(ii)}$
$\text{tan}\theta =\frac{a}{g};\text{a = g tan}\theta$