Time period of simple pendulum on earth's surface is ' T '. Its time period becomes ' xT ' when taken to a height R (equal to earth's radius) above the earth's surface. Then the value of ' x ' will be

Step-by-step solution

T =2 l ~g At a height 'h' from earth's surface, array ll & xT =2 l g_ h & x = g g _ h . .( i ) & Now, g _ h = GM ( R + h )^2 & g _ h = GM 4 R ^2 & g _ h = g 4 & From equations (i) and (ii), & x = g g / 4 = 4 =2 array From equations (i) and (ii), x= g g / 4 = 4 =2