A particle of mass m moving in the x - directionwith speed 2c is hit by another particleof mass2m moving in the y - direction with with speed v . If the collision is perfectly inelastic , the percentage loss in the enrgy during the collision is close to .

A particle of mass m moving in the x - directionwith speed 2c is hit b

1.	A particle of mass m moving in the x - directionwith speed 2c is hit by another particleof mass2m moving in the y - direction with with speed v . If the collision is perfectly inelastic , the percentage loss in the enrgy during the collision is close to .
Answer» 0.44 0.5 0.56 0.62 Solution :`VEC(p_(1))=m_(1)vec(v_(1)) =2MV hat(i)` `vec(p_(2)) =m_(2)vec(v_(2)) =m(2v)hat(i) =2mv hat(j)` ` :. " Resultant momentum " \| vec(p) \| = sqrt(p_(1)^(2)+p_(2)^(2))` `(2m+m) v. = sqrt((2mv)^(2)+(2mv)^(2))` ` : 3v. , = sqrt(4m^(2)v^(2)+4m^(2)v^(2))` ` :. 3v. m = 2sqrt(2) MV ` ` :. v = = (2sqrt(2))/3 v ` Now , DECREASE in K.E= INTIAL K.E - K.E after collision `1/2 m(2v)^(2) +1/2 (2m) v^(2) - 1/2 [2m+m] (v)^(2)` ` = 2,v^(2) +mv^(2)-1/2 xx3m xx (8v^(2))/9` ` = 3mv ^(2) - (4v^(2)m)/3 ` `= (9mv^(2)-4v^(2)m)/3= (5mv^(2))/3` ` :. %" loss in K.E "=((5mv^(2))/3)/(2mv^(2)+mv^(2)) xx100 % ` `=(5mv^(2))/(3xx3mv^(2)) xx100 % ` ` = 500/9 % ` ` = 55.55 % ` ` = 56 % `