if a ball is made along the diameter of earth and an iron ball is dropped from one end of the bore, how the bar will behave in the bore?
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Correct option is
C
2π
g
R
+4
g
2h
The ball is dropped from a point A at a height h above the surface. Thus during the entire motion, let the time taken by the ball to move move from A to B be t
1
, from B to C and C to B be t
2
, from C to D be t
3
, from D to C be t
4
, and from B to A be t
5
,
Let T be the time period of the complete motion.
Now for the motion A to B; h=0+
2
1
g(t
1
)
2
⟹t
1
=
g
2h
Similarly , t
3
=t
4
=t
5
=t
1
=
g
2h
As the time period of the particle executing SHM inside the tunnel is given by t=2π
g
R
e
Thus the time period of the motion of the ball inside the tunnel i.e B to C and C to B, t
2
=2π
g
R
Now the total time period of the motion T=t
1
+t
2
+t
3
+t
4
+t
5
⟹T=2π
g
R
+4
g
2h
solution