1.

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​

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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


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