Question

A block of mass $m$ is placed on a smooth wedge of inclination $\theta$. The whole system is accelerated horizontally so that the block does not slip on the wedge. The force exerted by the wedge on the block ($g$ is the acceleration due to gravity) will be

• A. $mg\cos \theta$
• B. $mg\sin \theta$
• C. $mg$
• D. $\frac{mg}{\cos \theta }$

Answer 1

The correct option is D $\frac{mg}{\cos \theta }$



Applying pseudo force on block


As block does not slip,
$ma\cos \theta =mg\sin \theta$
$a=g\tan \theta \dots \dots \left(1\right)$
$N=ma\sin \theta +mg\cos \theta$
$N=mg\tan \theta \sin \theta +mg\cos \theta$
$N=\frac{mg}{\cos \theta }$