A smooth sphere A of mass m collides elastica | vedclass

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(C) For an elastic collision between two identical masses where one is initially at rest,the velocity component along the line of impact is transferre

Vedclass · Accepted Answer

$(iii), (iv)$

Vedclass · Answer

(C) For an elastic collision between two identical masses where one is initially at rest,the velocity component along the line of impact is transferred entirely to the target sphere.Let $v = 8 \ m/s$. The component of velocity of $A$ along the line of centers (common normal) is $v \cos 60^{\circ} = 8 	imes 0.5 = 4 \ m/s$.The component of velocity of $A$ perpendicular to the line of centers is $v \sin 60^{\circ} = 8 	imes \frac{\sqrt{3}}{2} = 4\sqrt{3} \ m/s$.After the elastic collision,the velocity component along the line of centers is transferred to sphere $B$. Thus,sphere $B$ moves with speed $v_B = 4 \ m/s$ along the line of centers.Sphere $A$ retains its velocity component perpendicular to the line of centers,which is $v_A = 4\sqrt{3} \ m/s$.Since sphere $A$ has a velocity component perpendicular to the line of centers and sphere $B$ moves along the line of centers,their directions of motion are at right angles $(90^{\circ})$.Thus,statements $(iii)$ and $(iv)$ are correct.

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Statement-$1$: In an elastic collision between two bodies,the relative speed of the bodies after the collision is equal to the relative speed of the bodies before the collision.
Statement-$2$: In an elastic collision,the linear momentum of the system is conserved.

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