An ideal spring with spring-constant K is hung from the ceiling and a block of mass M is attached to its lower end. The mass is released with the spring initially unstretched. Then the maximum extension in the spring is

Question

An ideal spring with spring-constant K is hung from the ceiling and a block of mass M is attached to its lower end. The mass is released with the spring initially unstretched. Then the maximum extension in the spring is (A) 4 Mg/K (B) 2 Mg/K (C) Mg/K (D) Mg/2 K

Tardigrade Admin · Accepted Answer

Let x be the maximum extension of the spring. From energy conservation <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/73ab8ffef0d4d73b4c382eaa502f35ef-.png" /> Loss in gravitational potential energy = Gain in potential energy of spring M g x=(1/2) K x2 ⇒ x=(2 M g/K)

Q. An ideal spring with spring-constant $K$ is hung from the ceiling and a block of mass $M$ is attached to its lower end. The mass is released with the spring initially unstretched. Then the maximum extension in the spring is

4 Mg/K

2 Mg/K

Mg/K

Mg/2 K

Let x be the maximum extension of the spring. From energy conservation

Loss in gravitational potential energy
$=$ Gain in potential energy of spring
$M gx = \frac{1}{2} K x^{2}$
$\Rightarrow x = \frac{2 M g}{K}$

Q. An ideal spring with spring-constant K is hung from the ceiling and a block of mass M is attached to its lower end. The mass is released with the spring initially unstretched. Then the maximum extension in the spring is