Statement-1: Two particles of mass 1 kg and 3 kg move towards each other under their mutual force of attraction. No other force acts on them. When the relative velocity of approach of the two particles is `2 m//s`, their centre of mass has a velocity of `0.5 m//s`. When the relative velocity of approach becomes `3 m//s` the velocity of the centre of mass is `0.75 m//s`.
Statement-2: The total kinetic energy as seen from ground is `1/2muv_(rel)^(2)+1/2mv_(c)^(2)` and in absence of external force, total energy remains conserved.

Options

A. Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1.
B. Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1.
C. Statement-1 is true, statement-2 is false.
D. Statement -1 is false, statement -2 is true.

Answer

D

Explanation

`(K)=K+(K)=1/2(m+m) v^(2)+1/2muv^(2)`
`=1/2(4)(0.5)^(2)+1/2xx3/4(2)^(2)=2J`
`(K)=2=1/2xx4xxv^(2)+1/2(3/4)xx(3)^(2)`
`v^(2)=(-11)/16`]