Question

A massless spring of stiffness 400 N/m is fastened at left end to a vertical wall as shown in the figure I. initially block C of mass 2 kg and block D of mass 5 kg rest on horizontal surface with block C in contact with spring (But not compressiong it.) and the block D in contact with block C block C is moved leftward compressing spring by a distance of 0.5 m and held in place while block D remains at rest as shown in the figure. Now block C is released and it accelerates to the right towards block D the surface is rough and the coefficient of friction between each block and surface is 0.1 The block collide Instantaneously stick together and move right find the velocity of combined system just after collision.
A. 2 m/s
B. 3 m/s
C. 4 m/s
D. 6 m/s

Answer 1

Correct Answer - A
Using WET we can write
`(1)/(2)m_(C)v_(C)^(2)=(-K)/(2)(x_(f)^(2)-x_(i)^(2))-mum_(0)gd`
`impliesv_(C)=sqrt((kx_(i)^(2)-2mum_(C)gd)/(m_(e)))`
`v_(sys)=(m_(C)v_(C))/(m_(e)+m_(D))=2m//s`