Question

A block of mass m is pushed against a spring of spring constant k fixed at one end to a wall. The block can slide on a frictionless table as shown in fig. The natural length of the spring is $l_0$ and it is compressed to half of its natural length when the block is released. Then final velocity of the block will be:

• A. $\frac{l_0}{2}\sqrt{\frac{k}{m}}$
• B. $\frac{l_0}{4}\sqrt{\frac{k}{m}}$
• C. $\frac{1}{2}\sqrt{\frac{k{l}_0}{m}}$
• D. $\sqrt{\frac{k{l}_0}{2m}}$

Answer 1

The correct option is A $\frac{l_0}{2}\sqrt{\frac{k}{m}}$

Initially the compression of the spring is $\frac{l_0}{2}$. From conservation of energy,

$\frac{1}{2}k{\left(\frac{l_0}{2}\right)}^2=\frac{1}{2}m{v}^2$

calculating for $v$ will get,

$v=\sqrt{\frac{k}{m}}\frac{l_0}{2}$