Question

The length of a seconds pendulum is 1m on the earth. If the mass and diameter of the planet is double than that of the earth, then the length of the second's pendulum on the planet will be ______ 

Options

• 0.3 m

• 0.4 m

• 0.5 m

• 0.2 m

Answer 1

The length of a seconds pendulum is 1m on the earth. If the mass and diameter of the planet are double that of the earth, then the length of the second's pendulum on the planet will be 0.5 m.

Explanation:

`T_e/T_p = sqrt((ℓ_e)/(g_e)) xx sqrt((g_p)/(ℓ_p))`

But T_e = T_p

∴ `1 = sqrt((ℓ_e xx g_p)/(g_e xx ℓ_p))`

But g_p = `(G xx 2M)/(2R)^2 = (GM xx 2)/(4R^2) = g/2`

`g_eℓ_p = ℓ_e  g_p`

`ℓ_p = ℓ_e (g_p)/(g_e) = 1 xx 1/2 = 0.5  m`