Question

Two blocks of masses in and `4m` lie on a smooth horizontal surface connected with a spring in its natural length. Mass `m` is given velocity `v_(0)` through an impulse as shown in Fig. Which of the following is not true about subsequent motion?
A. Kinetic energy is maximum in ground frame and centre of mass (CM) frame simultaneously
B. Value of maximum and minimum kinetic energy is same in CM and ground frame
C. Minimum kinetic energy is zero in CM frame but non-zero in ground frame.
D. Maximum and minimum kinetic energy of m in ground frame is, respectively`1/2mv_(0)^(2)` and zero.

Answer 1

Correct Answer - B
In both `CM` and ground frame 1`K_(max)` is there when `x` is zero in spring, which occurs simultaneously.
`v_(CM)=(m(v_(0)+0))/(5m)=(v_(0))/5`
`K_(max) CM=1/2m((4v_(0))/5)^(2)+1/2(4m)((v_(0))/5)^(2)=2/5mv+(0)^(2)`
`K_(max) "ground "=1/2mv_(0)^(2)`
`K_(min CM)=0`
`K_(min) "ground"=1/2(m+4m)v_(CM)^(2)=(mv_(0)^(2))/10`
`K_(max m)=1/2 mv_(0)^(2)` (ground frame)
`K_(min) m=0` (ground frame when energy is shared by sping adn `4m` only and `m` will reverse direction of motion)