A block of mass M is attached to the lower end of a vertical spring. The spring is hung from a ceiling and has force constant value k. The mass is released from rest with the spring initially unstretched. The maximum extension produced in the length of the spring will be

Question

A block of mass M is attached to the lower end of a vertical spring. The spring is hung from a ceiling and has force constant value k. The mass is released from rest with the spring initially unstretched. The maximum extension produced in the length of the spring will be (A) 2Mg/k (B) 4Mg/k (C) Mg/2k (D) Mg/k

Tardigrade Admin · Accepted Answer

When the mass attached to a spring fixed at the other end is allowed to fall suddenly, it extends the spring by

x

. Potential energy lost by the mass is gained by the spring.

M gx = \frac{1}{2} k x^{2}

\Rightarrow x = \frac{2 M g}{k} .

Q. A block of mass M is attached to the lower end of a vertical spring. The spring is hung from a ceiling and has force constant value k. The mass is released from rest with the spring initially unstretched. The maximum extension produced in the length of the spring will be

2Mg/k

4Mg/k

Mg/2k

Mg/k

When the mass attached to a spring fixed at the other end is allowed to fall suddenly, it extends the spring by x. Potential energy lost by the mass is gained by the spring. Mgx=21​kx2 ⇒x=k2Mg​.

Q. A block of mass $M$ is attached to the lower end of a vertical spring. The spring is hung from a ceiling and has force constant value $k$ . The mass is released from rest with the spring initially unstretched. The maximum extension produced in the length of the spring will be

When the mass attached to a spring fixed at the other end is allowed to fall suddenly, it extends the spring by $x$ . Potential energy lost by the mass is gained by the spring.
$M gx = \frac{1}{2} k x^{2}$
$\Rightarrow x = \frac{2 M g}{k} .$