A particle of mass `m` moving eastward with a speed `v` collides with another particle of the same mass moving northward coalesce on collision. The new particle of mass `2 m` will move in the north - easterly direction with a velocity

Options

A. v
B. `v/2`
C. `v/(sqrt(2))`
D. `vsqrt(2)`

Answer

C

Explanation

By the principle of conservation of linear momentum,
Total momentum before collision = Total momentum after collision `:. m_(1)u_(1) + m_(2) u_(2) = ( m_(1)+m_(2))v`
`:. 1.67 xx 10^(-27) xx 10^(8) + 0 = ( 1.67 +3.34 ) xx 10^(-27) xx v`
`:. v = ( 1.67 xx 10^(-27) xx 10^(8))/((1.67 + 3.34 ) xx 10^(-27))`
`= ( 10^(8))/( 3) = 0.33 xx 10^(8) m//s`