Question

A thin spherical shell of total mass m and radius r is held fixed

Answer 1

Answer:

Lets divide the scenario into two steps:

1) Movement till the hole

2) Movement inside the spherical shell through hole

For step 1:

As energy is conserved, change in kinetic energy + change in potential energy =0

⇒(K

f

−K

i

)+(P

f

−P

i

)=0

⇒

2

mv

2

=

R

GMm

−

2R

GMm

Solving this we get v=(

R

GM

)

0.5

Now, for step 2:

Inside the shell, potential is constant and net force is zero.

So, it moves with constant velocity of v=(

R

GM

)

0.5

⇒ Time taken =

v

2R

=2(

GM

R

3

)

0.5

Hence, x=2