A simple pendulum of length 40 cm is taken inside a deep mine. Assume for the time being that the mine is 1600 km deep. Calculate the time period of the pendulum there. Radius of the earth = 6400 km.

1.47 s

given length

Let M be the mass of earth

--------->(1)

Gravity at depth ‘d’ will be

[Let ‘r’ be the distance from center of the earth to that point

]

---------->(2)

From (1) & (2)

[‘g’ on surface is ]

Time period at that depth

= 1.47 sec

1