Question

A particle of mass m moves in circular orbits with potential  energy V(r) = Fr, where F is a positive constant and r is its distance from the origin. Its energies are calculated using the Bohr model. If the radius of the particle's is denoted by R and its speed and energy are denoted b V and E, respectively, then for the n^th orbit (here h is the plank's constant)-

Answer 1

Correct answer is (B,C)

U = Fr 

[Using U = Potential energy and v = velocity, to avoid confusion between their symbols] 

⇒ Force =\(\frac{-dU}{dt}\)= – F 

⇒ Magnitude of force = Constant = F

⇒ F = \(\frac{mv^2}{R}\) ……(1) 

⇒ mvR = \(\frac{nh}{2π}\) ……(2)