Question

A spring of spring constant K is hanging from the ceiling of an elevator and an object of mass m is attached to the lower end. Whole system is in equilibrium at rest. The elevator starts moving upward with constant acceleration g. An observer in elevator frame observes that
i) Object is performing SHM of amplitude $\frac{mg}{K}$
ii) Object comes to rest after displacement of $\frac{mg}{K}$ downward from initial position
iii) Maximum displacement of object from initial position is $\frac{3mg}{K}$ (downward)
iv) Maximum displacement of object from initial position is $\frac{mg}{K}$ (upward)

• A. (i) and (ii)
• B. (ii) and (iv)
• C. Only (iii)
• D. (iii) and (iv).

Answer 1

The correct option is D

(iii) and (iv).

$2mg(x_2-x_1)=\frac{1}{2}K(x_2^2-x_1^2)(x_2-x_1)=\frac{4mg}{K}{x}_2=\frac{3mg}{K}$
Hence (iii) and (iv)