Two steel spheres approach each other head-on with the same speed and collide elastically. After the collision one of the spheres of radius r comes to rest,the radius of other sphere is
Answers
Answer
Option 'A' is correct
Let us consider m
1
& m
2
are masses of the sphere and velocity is v of the sphere before collision 'v' is the velocity of other sphere and fist sphere at rest after collision.
From conservation of energy
2
1
m
1
v
1
2
+
2
1
m
2
v
2
2
=
2
1
m
1
v
1
2
+
2
1
m
2
v
2
2
2
1
m
1
v
2
+
2
1
m
2
v
2
=
2
1
m
2
v
′2
....(1)
2
1
m
1
v
2
−
2
1
m
2
v
2
=
2
1
m
2
v
′2
v
′
=
m
2
n(m
1
−m
2
)
Put the value of v
′
in eq (1)
2
1
m
1
v
2
+
2
1
m
2
v
2
=
2
1
m
2
×(
m
2
v(m
1
−m
2
)
)
2
m
1
+m
2
=
m
2
(m
1
−m
2
)
2
m
1
m
2
+m
2
2
=m
1
2
+m
2
2
−2m
1
m
2
m
2
=
3
m
1
...(2)
The volume of the fiist sphere is v and the volume of other is v/3
Now, the radius of the sphere is r and other sphere is r
′
The volume of first sphere is
3
4
πr
′
3=
3
v
...(3)
the volume of radius other sphere is
3
4
πr
′
3=
3
v
....(4)
Divide eq. (4) by (3)
r
′
=
(3)
3
1
r
Answer:
#Hope you have satisfied with this answer.
