Gravitation Question 6

Question 6 - 25 January - Shift 1

$T$ 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:

(1) 4

(2) 2

(3) $\frac{1}{2}$

(4) $\frac{1}{4}$

Show Answer

Answer: (2)

Solution:

Formula: Effect of Altitude

At surface of earth time period

$T=2 \pi \sqrt{\frac{\ell}{g}}$

At height $h=R$

$g^{\prime}=\frac{g}{(1+\frac{h}{R})^{2}}=\frac{g}{4}$

$\therefore \quad xT=2 \pi \sqrt{\overline{(g / 4)}}$

$\Rightarrow xT=2 \times 2 \pi \sqrt{\frac{\ell}{g}}$

$\Rightarrow xT=2 T \Rightarrow x=2$