Question

spercial indecatries lies on the surface with radius?​

Answer 1

Answer:

Given,

Mass of chain is m

Length is l

Radius of sphere is R

⇒h=Rsinθ

⇒dl=Rdθ

The mass of dl length of the chain dm=mdl

Potential energy.

dU=(dm)gh

⇒dU=

l

mdl

gh=

l

mghdl

=

l

mgh

2

sinθdθ

⇒dU=

l

mgR

2

sinθdθ

On Integrating

U=∫

θ

2

x

l

mgR

2

sinθdθ

U=−

l

mgR

2

[cosθ]

θ

2

π

=−

l

mgR

2

[cos(

2

π

)−cosθ]

U=−

l

mgR

2

cosθ=

l

mgR

2

sin(

R

l

)

Hence, potential energy is

l

mgR

2

sin(

R

l

)