Question

A thin circular ring first slips down a smooth incline then rolls down a rough incline of identical geometry from same height. Ratio of time taken in the two motion is a) 1/2 b)1 c)1/​√2 d) 1/4

Answer 1

Answer:

Option C is correct option

Explanation:

case (i) Transitional motion

acceleration=gsinθ

case (ii) acceleration =

1+

MR

2

1

gsinθ

I=MR

2

a=

2

gsinθ

Now using ρ=ut+

2

1

at

2

a

1

t

1

2

=a

2

t

2

2

θ&ρsameforbothare&v=0

t

2

2

t

1

2

=

a

1

a

2

=

2gsinθ

gsinθ

t

2

t

1

=

2

1

∴

t

2

t

1

=

2

1

.