Question

Two uniform solid spheres having unequal masses and unequal radii are released from rest from the same height on a rough incline. If the spheres roll without slipping,
(a) the heavier sphere reaches the bottom first
(b) the bigger sphere reaches the bottom first
(c) the two spheres reach the bottom together
(d) the information given is not sufficient to tell which sphere will reach the bottom first.

Answer 1

Answer:

Work-energy theorem, mgh=

2

1

mv

2

+

2

1

Iw

2

Also v=rw and for sphere I=

5

2

mr

2

⟹gh=

2

1

v

2

+

5

1

v

2

gh=

10

7

v

2

implies v is same for both the spheres.

Also acceleration, a=

1+K

gsinθ

which is also same for both spheres.

Thus both will reach the bottom together.