Question

Consider the above system, in which a mass $m$ is balanced on a FRICTIONLESS incline with the help of a vertical cord exerting tension $T$ directly upwards on the mass.
What is the normal force $F_N$ exerted by the incline on $m$?
The incline makes an angle of ${30.0}^o$ with the horizontal.

• A. $F_N=0$
• B. $F_N=mg-T$
• C. $F_N=\frac{mg-T}{\sin \theta }$
• D. $F_N=mg\tan \theta$
• E. $F_N=T\tan \theta$

Answer 1

The correct option is A $F_N=0$

Resolving the tension force and the gravitational force along the inclined plane and perpendicular to it.

Along the inclined plane : $mg$ $sin\theta =T$ $sin\theta$ $⟹T=mg$ ........(1)

Perpendicular to the plane : $Tcos\theta +F_N=mgcos\theta$

$⟹$ $F_N=(mg-T)$ $cos\theta =0$ (using 1)