A particle is moving with uniform speed along the circumference of a circle of radius R under the action of a central fictitious force F which is inversely proportional to R 3 . Its time period of revolution will be given by :

Question

A particle is moving with uniform speed along the circumference of a circle of radius R under the action of a central fictitious force F which is inversely proportional to R 3 . Its time period of revolution will be given by : (A) T propto R 2 (B) T propto R (3/2) (C) T propto R (5/2) (D) T propto R (4/3)

Tardigrade Admin · Accepted Answer

F propto (1/R3) (K/R3)=m ω2 R ω2=(K/m) × (1/R4) ((2 π/T))2=(K/m) × (1/R4) T2 propto R4 T propto R2

Q. A particle is moving with uniform speed along the circumference of a circle of radius $R$ under the action of a central fictitious force $F$ which is inversely proportional to $R^{3} .$ Its time period of revolution will be given by :

$T \propto R^{2}$

$T \propto R^{\frac{3}{2}}$

$T \propto R^{\frac{5}{2}}$

$T \propto R^{\frac{4}{3}}$

$F \propto \frac{1}{R ^{3}}$
$\frac{K}{R ^{3}} = m ω^{2} R$
$ω^{2} = \frac{K}{m} \times \frac{1}{R ^{4}}$
$(\frac{2 π}{T})^{2} = \frac{K}{m} \times \frac{1}{R ^{4}}$
$T^{2} \propto R^{4}$
$T \propto R^{2}$

Q. A particle is moving with uniform speed along the circumference of a circle of radius R under the action of a central fictitious force F which is inversely proportional to R3. Its time period of revolution will be given by :

T∝R2

T∝R23​

T∝R25​

T∝R34​