Question

Check the correctness of formula t=2π √m/k, dimensionally​

Answer 1

Hi there! Lets see!

• m is mass, and its units are kg
• k is the elastic constant measured in newtons per meter (N/m), or kilograms per second squared kg/s²

Therefore:

`\sqrt{(m)/(k)} =\sqrt{([kg])/([(kg)/(s^2)])} =\sqrt{([kg])/([kg])\cdot s^2} = √([s]^2) = s`

The period is given in seconds so the formula is dimensionally​ correct.