Given:
The final velocity of the first sphere,
v1=u1u2=0 (the second sphere is at rest)
The mass of a sphere is proportional to the cube of its radius:
m∝R3Let
m1 and
m2 be the masses, and
R1 and
R2 be the radii of the first and second spheres.
Step 1: Use the formula for an elastic collision
After the collision, the velocity of the first sphere is:
v1=Step 2: Substitute
u2=0v1=We know
v1=u1 :
u1=Divide both sides by
u1 (since
u1≠0 ):
= Step 3: Solve for
m1 in terms of
m2Multiply both sides by (
m1+m2 ):
7(m1+m2)=9(m1−m2)7m1+7m2=9m1−9m27m2+9m2=9m1−7m116m2=2m1m1=8m2Step 4: Relate masses to radii
Since mass of a sphere,
m∝R3 :
=()38=()3Step 5: Solve for
R2Take the cube root of both sides:
=2R1=2R2 R2=Plug in
R1=1.2cm :
R2==0.6cm
