Pseudo force

Question

A block of mass *m* is placed on a smooth inclined wedge *A B C* 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

Moderate

Solution

In non-inertial frame,

$N\mathrm{sin}\theta =ma........\left(i\right)$

$N\mathrm{cos}\theta =mg.........\left(ii\right)$

From *(i)* and *(ii)*,

$\begin{array}{l}\mathrm{tan}\theta =\frac{a}{g}\\ a=g\mathrm{tan}\theta \end{array}$

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