A spring, which is initially in its unstretched condition, is first stretched by a length x and then again by a further length x. The work done in the first case is W_1 and in the second case is W_2. Then

A spring, which is initially in its unstretched condition, is first st

1.	A spring, which is initially in its unstretched condition, is first stretched by a length x and then again by a further length x. The work done in the first case is W_1 and in the second case is W_2. Then
Answer» `W_2 = W_1` `W_2 = 2W_1` `W_2 = 3W_1` `W_2 = 4 W_1` SOLUTION :Let K be the force constant of the spring. Potential energy of the spring after the first STRETCHING is `U_1 = 1/2 kx^2` Potential energy of the spring after the second stretching is `U_2 = 1/2 k (2x)^2` `:. W_1 = U_1 = 1/2 kx^2` and `W_2 = U_2 - U_1 = 1/2 k(2x)^(2) - 1/2 kx^2 = 3(1/2 kx^2) = 3W_1`.