Question

a. The centripetal force depends on the mass of the body, velocity, and radius of a circular path. Find the expression for the centripetal force acting on the body using the principle of dimensional analysis. (Take constant k= 1)
b. When the planet Jupiter is at a distance of 824.7 million kilometres from the Earth, its angular diameter is measured to be 35.72” of an arc. Calculate the diameter of a Jupiter.​

Answer 1

Answer:

 F=k(m)x(v)y(r)zF=k(m)x(v)y(r)z

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

[MLT−2]=[M]x[LT−1]y[L]z[MLT-2]=[M]x[LT-1]y[L]z

=[MxLy+zT−y]=[MxLy+zT-y]

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

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

or z=1−y=−1z=1-y=-1

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

F=kmv2r−1=kmv2rF=kmv2r-1=kmv2r F=mv2rF=mv2r (where k=1)