A voltmeter has a range 0−V with a series resistance R. With a series resistance 2R, the range is 0−V'. The correct relation between V and V' is

For conversion of galvanometer (of resistances) into voltmeter, a resistance is connected in series.∴     ig =VR+G   and   ig =V'2R+G⇒   VR+G = V'2R+G⇒   V'V=2R+GR+G = 2R+G−GR+G=2−GR+G  ⇒  V'=2V−VGR+G  ⇒ V'<2V