Question

A block of mass m is revolving in a smooth horizontal plane with a constant speed v. If the radius of the circular path is R, find the total contact force received by the block.

• A.
• B. mg
• C.
• D.

Answer 1

The correct option is D

FBD: Let $N_1,N_2\uparrow$ be the normal reactions offered by the vertical and horizontal surfaces respectively, $N_1$ pushes the block towards the centre of circle and $N_2$ equilibrate the block in vertical by nullifying the weight $m{g}^{-2}$

Force equation:

$N_1=m{a}_r=\frac{m{v}^2}{R}$ ....................(i)

$N_2=mg$ ........................(ii)

Hence the net reaction (contact) force is

$\stackrel{\rightharpoonup }{N}=\stackrel{\rightharpoonup }{N_1}+\stackrel{\rightharpoonup }{N_2}$

$\mid N\mid =\mid \stackrel{\rightharpoonup }{N}+\stackrel{\rightharpoonup }{N}\mid =\sqrt{N_2^2+N_1^2}$

Substituting $N_1$ and $N_2$ we have N = m = $\sqrt{\frac{v^4}{R^2}+g^2}$