The speed of transverse waves in a string under tension T and mass m per unit lemgth of a wire is v if the string is replaced by another string of radius half to the original string the speed of wave becomes A)2v B)4V C)V/2 D)V/4

If the radius of the sting is half that if the original string (let it be r). then area becomes 1/4th the initial. So as per the formula for velocity of a wave on stringv=√(T/u). where is mass per unit area. So according to this, the velocity of the string:V=√(T/u÷4)V=√(4T/u)V=2v