If the angular speed of the earth is doubled,the value of acceleration due to gravity $(g)$ at the north pole:

$A$ body weighs $72 \, N$ on the surface of the earth. When it is taken to a height of $h = 2R$,where $R$ is the radius of the earth,it would weigh ........ $N$.

The weight of a body at the surface of earth is $18 \, N$. The weight of the body at an altitude of $3200 \, km$ above the earth's surface is $........ \, N$ (given,radius of earth $R_e = 6400 \, km$).

$A$ simple pendulum is placed at a place where its distance from the earth's surface is equal to the radius of the earth. If the length of the string is $4 \ m$,then the time period of small oscillations will be . . . . . . $s$. [Take $g = \pi^2 \ ms^{-2}$]

The variation of acceleration due to gravity $(g)$ with distance $(r)$ from the center of the earth is correctly represented by ... (Given $R =$ radius of earth)

If a particle takes $t$ seconds less and acquires a velocity of $v \text{ m/s}$ more in falling through the same distance on two planets,where the accelerations due to gravity are $2g$ and $8g$ respectively,then: