Question

the time period of a simple pendulum is T. is the length of pendulum is increased by 44% then the time period becomes ?
(a) 1T
(b) 1.2T
(c) 1.44T
(d) 4T

Answer 1

Time period of a simple pendulum at surface of earth is given by [T=2π√(l/g)] where g=acceleration due to gravity so now if the length is increased by 44%. New length= 1.44l.






Period T ( time of a pendulum ) = 2 x Pi x ( length , l / g , acceleration due to gravity ) !/2 , where g =9.80 m/sec2. 
Let us assume original length of a pendulum l1 to be = 1 then 44% increase in length of in l1 would be = 1.44, so peiodic time of a pendulum with oiginal length l1= 1 would be: 2x Pi x ( 1/9.80)^1/2 = 44/7 x 0.319438282 , similarly we can find periodicity of a pendulum with 1.44 length = 44/7 x ( 1.44/9.80)^1/2 = 44/7 x 0.383325939 . 
so change in time increses : 0.383325939/ 0.319438282 = 1.20 times ( since 44/7 is a common factor in both cases it is eliminated)