We know,time period of a pendulum is #T= 2pi sqrt(L/g)# ,where, #L# is the length of the pendulum
If,length is decreased #2# times i.e made half the initial(#L'=L/2#),new time period becomes, #T'= T/sqrt(2)#
Now,energy of a simple pendulum #prop 1/2 m omega^2 (L )^2# (using, #E=1/2 m omega^2 A^2#,where, #omega# is the angular frequency and #A# is the amplitude of motion,for a simple pendulum, it is #L #)
So,#omega^2*L^2 = (2pi)^2/T^2 *L^2#
So,energy #prop L^2/T^2#
So,we can say, #(E')/E = ((L')/(T'))^2 (T/L)^2# (where, all the values with #'# sign means final values)
So,putting the values we get, #E' = E/2#
