T is the time period of simple pendulum on the earth's surface. Its time period becomes x T when taken to a height R (equal to earth's radius) above the earth's surface. Then, the value of x will be :

Solution

Physics sir · 3 steps

At height R you are twice as far from the centre, so g drops to a quarter and T doubles.

1. Gravity at height. Gravity falls off as the square of the distance from the earth's centre. At height h, gₕ = g(R/(R+h))².
2. Height equals R. The distance from the centre becomes 2R, so gₕ = g(R/2R)² = g/4.

   T'/T = √(g/gₕ) = √(g/(g/4)) = 2

3. So. Since T = 2π√(l/g), a quarter of the gravity gives twice the time period. So T' = 2T and x = 2, option (c).

The idea to keep. The time period goes as 1/√g. Find how g changes first, then take the square root of the inverse ratio. Height is measured from the surface, distance from the centre.

Answer from the NTA final answer key. Solution by PrepWiser.