A body of mass 2 kg is placed on a horizontal frictionless surface . It is connected to one end of the a spring whose force constant is 250 N/m the other end of the spring is joining with the wall A particle fo mass 0.15 kg moving horizontally with speed V sticks to the body after collision if it compressess the spring by 10 cm the velocity of the pariticle is -

Options

A. 3 m/s
B. 5 m/s
C. 10 m/s
D. 15 m/s

Answer

D

Explanation

BY the conservation of momentum
`mxxv=(m+M)V`
by the conservation of enrgy
`(1)/(2)kx^(2)=(1)/(2)(m+M)V^(2)`
` =(1)/(2)(m+M)((mv)/(m+M))^(2)`
` implies v= sqrt((kx^(2)(m+M))/(m^(2)))`
`=(x)/(m)sqrt(k(m+M))`
So v= 15 m/s