A stone is rotated steadily in a horizantal circle with a period T by a string of length L. If the tension in the stringis constant and L increases by 1% find the percentage change in T.

Answer 1

centripetal acceleration = a = v^2/L
Period = T = 2 x pi x L / v
m = mass of stone
tension = f = m x a
L1 = L x 1.01
if f and m are constant, then a is constant. Then
v1 = sqrt(a x L1)
T1 = 2 x pi x L1/v1
percentage change = 100x(T1-T)/T