Two blocks P and Q of masses 0.3 kg and 0.4 kg respectively are stuck to each other by some weak glue as shown in the figure. They hand together at the end of a spring with a spring constant `"k = 200 N m"^(-1)`. The block Q suddenly falls free due to failure of glue, then find the maximum kinetic energy of the block P during subsequent motion (in mJ).

Answer

40

Explanation

Let A be the amplitude, then we have
`kA = mg implies A = (mg)/(k)`
` A = ( 0. 4 g )/ (200) = 2 cm`
Motion starts from the lower extreme.
`KE _(max) = (1)/(2) m omega ^(2) A ^(2) = (1)/(2) xx 0.3 xx (k)/(m) xx A ^(2) `
`= (1)/(2) xx 0.3 xx (200)/(0.3) xx ((2)/(100)) ^(2) = 0.04 J = 40 mJ`