Question

if the radii of circular paths of two particles of same masses are in the ratio 2 is to 3 then to have a constant centripetal force their velocity should be in the ratio of.

Answer 1

• Given :

Ratio of mass M1/M2 = 2/3

• To Find :

Ratio of Velocity = V1/V2 = ?

• Formula :

Centripetal Force = MV^2/R

; where, M = Mass os particle executing

circular motion

V = Velocity

R = Radius of circular mass

; Here, R and F is constant....

; So, MV^2 = Constant

• Calculation :

M1V1^2 = M2V2^2

M1/M2 = V2^2/V1^2

(2/3)^1/2 = V2/V1

• Answer :

V1/V2 = (3/2)^1/2

Answer 2

Answer:

If the radii of circular paths of two particles of the same masses are in the ratio 2:3 then to have a constant centripetal force their velocity should be in the ratio of $1:\sqrt{2}$

Explanation:

A force that keeps an object in circular motion is called the centripetal force that is given by the formula $F=mv^{2}/r$

where $m$ - the mass of the object

$v$ - velocity of the object

$r$ - radius of the circular orbit

From the question, we have two-particle with the same masses $m_{1} =m_{2}$

the ratio of their radii $r_{1} :r_{2} =2:3$

to have constant force means

$F_{1} =F_{2}$

$\frac{m_{1}v_{1} ^{2} }{r_{1} } =\frac{m_{2} v_{2} ^{2} }{r_{2} }$

substitute the given values we get

$\frac{v_{1} ^{2} }{v_{2} ^{2} } =r_{1}/r_{2}=1/2$

$v_{1}:v_{2} =1:\sqrt{2}$