Variation of G Due to Height and Depth

Q.

The value of g will become $10\%$ of its value at the earths surface at a height _____ above the surface of Earth.

Q.

If the distance between centers of earth and moon is D and the mass of earth is 81 times the mass of moon, then at what distance from centre of earth the gravitational force will be zero

1. $\frac{D}{2}$

2. $\frac{2D}{3}$

3. $\frac{4D}{3}$

4. $\frac{9D}{10}$

Q.

What is the acceleration due to gravity at a height equal to $\frac{R}{2}$ from the Earth’s surface?

1. $\frac{3g}{4}$

2. $\frac{4g}{3}$

3. $\frac{9g}{4}$

4. $\frac{4g}{9}$

Q. If the value of ‘g’ at a height h above the surface of the earth is the same as at a depth x below it, then (both x and h being much smaller than the radius of the earth)

1. $x=h$
2. $x=2h$
3. $x=\frac{h}{2}$
4. $x=h^2$

Q.

The angular velocity of the earth with which it has to rotate so that acceleration due to gravity on ${60}^{\circ }$ latitude becomes zero is (Radius of earth = 6400 At the poles g = 10$m{s}^{-2}$)

1. $2.5\times {10}^{-3}rad/sec$

2. $5.0\times {10}^{-1}rad/sec$

3. $10\times {10}^{1}rad/sec$

4. $7.8\times {10}^{-2}rad/sec$

Q.

Weightlessness experienced while orbiting the Earth in International Space Station, is the result of

1. inertia

2. acceleration

3. zero gravity

4. free fall towards Earth

Q. A body weighs $200N$ on the surface of the earth. How much will it weight halfway down to the centre of the earth ?

1. $150N$
2. $200N$
3. $250N$
4. $100N$

Q.

The atmosphere is held to the earth by_________.

1. winds

2. gravity

3. clouds

4. ocean

Q. At what angular speed the Earth should rotate, so that effective acceleration due to gravity at ${45}^{\circ }$ latitude becomes half of effective acceleration due to gravity at pole? (Radius of earth is $R$ and acceleration due to gravity without taking variation of Earth’s rotation at surface is $‘g^{\prime }$)

1. $\omega =\sqrt{\frac{g}{R}}$
2. $\omega =\sqrt{\frac{g}{2R}}$
3. $\omega =\sqrt{\frac{2g}{R}}$
4. $\omega =\sqrt{\frac{3g}{4R}}$

Q. If the value of ‘g’ at a height h above the surface of the earth is the same as at a depth x below it, then x is equal to.

1. h
2. 2h
3. $\frac{h}{2}$
4. 4h

Q. A particle hanging from a spring stretches it by $1\text{cm}$ at earth’s surface. How much will be the same particle stretch (in cm) the spring at a place $800\text{km}$ above the earth’s surface? (Take the radius of the earth as $6400\text{km}$)

Q. A spring balance is graduated on sea level. If a body is weighed with this balance at consecutively increasing heights from earth's surface, the weight indicated by the balance:

1. Will go on increasing continuously
2. Will go on decreasing continuously
3. Will remain same
4. Will first increase and then decrease

Q. The height at which the acceleration due to gravity becomes $\frac{g}{9}$ (where g = the acceleration due to gravity on the surface of th earth) in terms of $R$, radius of the earth is

1. $2R$
2. $\frac{R}{\sqrt{3}}$
3. $\frac{R}{2}$
4. $\sqrt{2}R$

Q.

Weight of a body of mass m decreases by $1\%$ when it is raised to height h above the earth’s surface. If the body is taken to a depth h in a mine, change in its weight is

1. $2\%decrease$

2. $0.5\%decrease$

3. $1\%increase$

4. $0.5\%increase$