A block attached with an ideal spring is kept on a smooth horizontal surface. Now the free end of the spring is pulled with a constant velocity `u` horizontally. Then the maximum energy stored in the spring and bock system during subsequent motion is `:`

Options

A. `(1)/(2)m u^(2)`
B. `m u^(2)`
C. `2 m u^(2)`
D. `4 m u^(2)`

Answer

C

Explanation

As`,W_(ext)=Delta(ME),ME=` Mechanical energy.
Mechanical energy will keep on inncreasing upto the instant the `W_(ext)` is positive, which will happen till there is no compression in the spring . First the spring gets extended to a maximum and after which the extension decreases upto the natural length. After that there is a compression in the spring, results in a `-ve` external work `(` so as to move the end of spring at constant speed `u)`.
Hence maximum energy stored is at the natural length.
`& ME_(max)=(1)/(2) mv^(2)`
At the natural length `v=2u`, since th block is movin at this instant at a speed `u ` with respect to the other end of the spring.
Hence `ME_(max)=(1)/(2) m (2u)^(2)= 2 m u ^(2)`.