An ideal spring with spring-constant is hung from the ceiling and a block of mass is attached to its lower end. The mass is released with the spring initially unstretched. Then the maximum extension in the spring is [2002]

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 [2002]

Smart Achievers · Accepted Answer

(2)

Let $M$ be the maximum extension of the string. Here mechanical energy is conserved, so decrease in the gravitational potential energy of spring mass system $(M g x)$

= gain in spring elastic potential energy $(\frac{1}{2} k x^{2})$

$M g x = \frac{1}{2} k x^{2} \Rightarrow x = \frac{2 M g}{k}$

Solution

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 [2002]

1 $\frac{4 M g}{k}$

2 $\frac{2 M g}{k}$

3 $\frac{M g}{k}$

4 $\frac{M g}{2 k}$

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Solution

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 [2002]

1 4Mgk

2 2Mgk

3 Mgk

4 Mg2k