Question

What would be the length of a sec. pendulum at a planet (where acc. due to gravity is g/4) if it’s length on earth is l(a) l/2(b) 2l(c) l/4(d) 4l

Answer 1

Given :

Length of pendulum on earth = l

Acceleration due to gravity on other planet = g/4

To Find :

The length of the pendulum on other planet = ?

Solution :

• The time period of a pendulum is given by the relation

         $T=2\pi \times\sqrt{\frac{l}{g} }$

• For a seconds pendulum the time period of the pendulum is one sec in both the cases

        $T=2\pi \times\sqrt{\frac{l_{1} }{g_{1}} }\rightarrow Equation(1)$

        $T=2\pi \times\sqrt{\frac{l_{2} }{g_{2}} }\rightarrow Equation(2)$

• By diving the equations we get

        $\frac{l_{1}}{g_{1}} = \frac{l_{2}}{g_{2}}$

        $\frac{l}{g} =\frac{l_{2}}{\frac{g}{4}}$

        $l_{2} = \frac{l}{4}$

The length of the object at that planet is l/4