the time period of an object depends upon density , radius and surface tension. derive an equation for it.

you have to apply dimensions.

see dimensionless constants cannot be determined by this method. so you have to account for them by including the factor k.

k is a dimensionless quantity.

it is basically a constant.

so it comes out to be T = kρ^1/2R^3/2T^-1/2.

IT COMES BY SOLVING A SYSTEM OF THREE EQUATIONS WITH THREE UNKNOWNS WHICH ARE BASICALLY THE POWERS IN THE EXPRESSION OF TIMEPERIOD IN TERMS OF THE MENTIONED QUANTITIES. JUST WRITE THE DIMENSIONS OF LHS AND RHS AND EQUATE THEM TO GET THESE POWERS.