Question

i) the force "F" acting on a body of
mass "m', moving with velocity along
the circumference of a circle of radius r
establish relationship between force
and mass, velocity and radius if F depends
these quantities. We dimensions
analysis.
​

Answer 1

Answer:

The centripetal force F acting on a particle moving uniformly in a circle may depend. upon mass (m), velocity (v), and radius (r) of the circle.

Answer 2

Answer:

The force F acting on a body with mass m and velocity v is the rate of change of momentum: F=(d/dt)(mv). If m is constant, this becomes F=ma, where a=dv/dt is the acceleration. But in the theory of relativity the mass of a particle varies with v as follows: m=m0/√1−v2/c2.

Explanation:

From the given figure,

The resultant of the forces F

1

and F

2

will be =

2

F.

Now,

Since F

3

is 135

o

to F

2

and resultant of F

1

andF

2

is 45

o

to F

1

i.e. both are in exactly opposite direction,

So total force acting on the body will be F

t

=F

3

−(resultant of F

1

andF

2

)

i.e. F

t

=

2

F−F=F(

2

−1)

So the acceleration on the body due to these three forces will be

a

f

=F

t

/m=(

2

−1)F/m=(

2

−1)ma/m=(

2

−1)a .