Question

Assume there are two identical simple pendulum clocks. Clock - 1 is placed on the earth and Clock - 2 is placed on a space station located at a height h above the earth's surface. Clock - 1 and Clock - 2 operate at time periods 4 s and 6 s respectively. Then the value of h is ______.

(consider the radius of earth R_E = 6400 km and g on earth 10 m/s²)

विकल्प

• 1200 km

• 1600 km

• 3200 km

• 4800 km

Answer 1

Assume there are two identical simple pendulum clocks. Clock - 1 is placed on the earth and Clock - 2 is placed on a space station located at a height h above the earth's surface. Clock - 1 and Clock - 2 operate at time periods 4 s and 6 s respectively. Then the value of h is 3200 km.

Explanation:

`T ∝ 1/sqrtg` and `g ∝ 1/(R + h)^2`

`T_1/T_2 = sqrt(g^'/g) = sqrt(R^2/(R + h)^2)`

`T_1/T_2 = 4/6 = R/((R + h)) ⇒ h = 3200` km