CBSE Class 11 Physics Chapter 8: Gravitation NCERT Solutions

(a) No, a body cannot be shielded from the gravitational influence of nearby matter. Unlike electrical forces, which can be shielded by conductors, gravitational force is independent of the medium and the nature of the intervening objects. Therefore, placing a body inside a hollow sphere or using any other means will not block the gravitational pull from external masses.

(b) Yes, if the space station is large enough, the astronaut might be able to detect gravity. This is because gravity varies slightly with distance from the Earth's center. If the spaceship is large, different parts of the astronaut's body would be at slightly different distances from the Earth, leading to a detectable difference in gravitational force across their body.

(c) The tidal effect of a celestial body depends on the difference in gravitational force exerted on the near and far sides of the object. This difference is inversely proportional to the cube of the distance ($1/d^3$), whereas the gravitational force itself is inversely proportional to the square of the distance ($1/d^2$). Although the Sun exerts a greater gravitational force on the Earth than the Moon, the Moon is significantly closer to the Earth. Due to this closer proximity, the Moon's tidal effect, which depends on the inverse cube of the distance, is greater than the Sun's tidal effect.

Acceleration due to gravity decreases with increasing altitude. As altitude increases, the distance from the Earth's center increases, and according to Newton's law of gravitation, the acceleration due to gravity decreases.

Acceleration due to gravity decreases with increasing depth. For a point inside the Earth at a depth $h$ from the surface (or a distance $r\; =\; R\_e\; -\; h$ from the center, where $R\_e$ is the Earth's radius), the acceleration due to gravity is given by $g\_h\; =\; g\; \backslash left(1\; -\; \backslash frac\{h\}\{R\_e\}\backslash right)$. As $h$ increases (depth increases), $g\_h$ decreases.

Acceleration due to gravity is independent of the mass of the body. While the gravitational force exerted by the Earth depends on the mass of the body ($F\; =\; G\; \backslash frac\{Mm\}\{r^2\}$), the acceleration due to gravity ($g\; =\; \backslash frac\{F\}\{m\}\; =\; G\; \backslash frac\{M\}\{r^2\}$) does not depend on the mass of the object experiencing the gravity.

The formula $-G\; Mm(1/r\_2-1/r\_1)$ is more accurate. This formula is derived directly from Newton's law of universal gravitation and is valid for any two points at distances $r\_1$ and $r\_2$ from the center of the Earth. The formula $mg(r\_2-r\_1)$ assumes that $g$ is constant, which is only a valid approximation for small changes in altitude near the Earth's surface.