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Claussen

the centripetal force acting on a particle moving in a circle depends on the mass(m) of the particle it's velocity(v) and radius(r) of the circle. derive dimensionally the formula for force.​

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186 cents Nenris
Answer:

Answer:

Let F=k(m)  

x

(v)  

y

(r)  

z

 

Here, k is a dimensionless constant of proportionality. Writing the dimensions of RHS and LHS in Eq. (i), we have

[MLT  

2

]=[M]  

x

[LT  

−1

]  

y

[L]  

z

=[M  

x

L  

y+z

T  

−y

]

Equation the powers of M, L and T of both sides, we have,

x=1,y=2andy+z=1

or z=1−y=−1

Putting the values in Eq. (i), we get

F=kmv  

2

r  

−1

=k  

r

mv  

2

 

 

F=  

r

mv  

2

 

 (where k=1)

244
Nenris
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