The highest temperature,density,and pressure on Earth are found:

Assume that the Earth is a solid sphere of uniform density and a tunnel is dug along its diameter throughout the Earth. It is found that when a particle is released in this tunnel, it executes a simple harmonic motion. The mass of the particle is $100 \, g$. The time period of the motion of the particle will be (approximately) (take $g = 10 \, m/s^2$, radius of Earth $R = 6400 \, km$):

$A$ ball is launched from the top of Mt. Everest,which is at an elevation of $9000 \, m$. The ball moves in a circular orbit around the Earth. Acceleration due to gravity near the Earth's surface is $g$. The magnitude of the ball's acceleration while in orbit is

Given below are two statements: one is labelled as Assertion $(A)$ and the other is labelled as Reason $(R).$
Assertion $(A):$ Time period of a simple pendulum is longer at the top of a mountain than that at the base of the mountain.
Reason $(R):$ Time period of a simple pendulum decreases with increasing value of acceleration due to gravity and vice-versa.
In the light of the above statements,choose the most appropriate answer from the options given below:

Assume that a tunnel is dug through the Earth from the North Pole to the South Pole and that the Earth is a non-rotating,uniform sphere of density $\rho$. The gravitational force on a particle of mass $m$ dropped into the tunnel when it reaches a distance $r$ from the center of the Earth is:

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: