# Variation of G Due to the Rotation of Earth

## Trending Questions

**Q.**A satellite can be in a geostationary orbit around the earth at a distance r from the centre. If the angular velocity of earth about its axis doubles, a satellite can now be in a geostationary orbit around earth if its distance from the center is

- r2
- r2√2
- r(4)1/3
- r(2)1/3

**Q.**

Difference between centre of mass and centre of gravity ?

**Q.**if the radius of earth shrinks by 2% , mass remaining constant, then how would the value of acceleration due to gravity change.

witn simple method

**Q.**The ratio of the weights of a body on the Earth’s surface to that on the surface of a planet is 9:4. The mass of the planet is (19)th of that of the Earth. If R is the radius of the earth, what is the radius of the planet ? (Take the planets to have the same mass density).

- R2
- R3
- R4
- R9

**Q.**If the angular momentum of a planet of mass m, moving around the Sun in a circular orbit is L, about the centre of the Sun, its areal velocity is:

- Lm
- 4Lm
- L2m
- 2Lm

**Q.**

The mass density of a spherical galaxy$K$ varies$K/r$ over a large distance$r$ from its center. In that region, a small star is in a circular orbit of radius$R$. Then the period of a revolution$T$ depends on$R$ as:

${T}^{2}\propto R$

${T}^{2}\propto {R}^{3}$

${T}^{2}\propto {\left(1/R\right)}^{3}$

$T\propto R$

**Q.**

The average density of the earth

The complex function of g

Does not depend on g

Inversely proportional to g

Directly proportional to g

**Q.**

a stone dropped from a height h reaches at the earth surface in 1 second. If the same stone is taken to the moon and drop freely from a height h then in what time will it reach the ground?

**Q.**

Obtain the mass of earth from the following data:

$g=9.8m{s}^{-2}\phantom{\rule{0ex}{0ex}}R=6.38\times {10}^{6}m\phantom{\rule{0ex}{0ex}}G=6.67\times {10}^{-11}M.K.S.units.$

**Q.**

Find the acceleration due to gravity at a height equal to half the radius of the earth, if g$g=9.8m{s}^{-2}$.

**Q.**

Why does the weight of an object change from place to place?

**Q.**An astronaut orbiting in a spaceship round the earth has a centripetal acceleration of 2.45 m/s2. The height of the spaceship from earth's surface is

(R= radius of earth )

- 3R
- 2R
- R
- R/2

**Q.**A solid sphere of mass M and radius R has a spherical cavity of radius R2 such that the centre of cavity is at a distance R2 from the centre of the sphere. A point mass m is placed inside the cavity at a distance R4 from the centre of sphere. The gravitational force on mass m is

- GMmR2
- GMm2R2
- 2GMmR2
- GMm4R2

**Q.**

Three spheres, each of mass M and radius R, are arranged as shown in the figure. Then the moment of inertia of the system about YY1

^{}

**Q.**

A planet moves around sun in nearly circular orbit period of revolution 't', radius of orbit r mass of sun m.

Time period if direcyly proportional to mass of sun, distance between planet and sun and universal gravitational constant.

Prove T^{2} is directly proportional to r^{3}

**Q.**

If $M$ is the mass of the earth and $R$ its radius, the ratio of the acceleration due to gravity and the gravitational constant is

$\frac{{R}^{2}}{M}$

$\frac{M}{{R}^{2}}$

$M{R}^{2}$

$\frac{M}{R}$

**Q.**A body of mass 1 kg is projected from ground at an angle 30 degree with horizontal on a level ground at a speed 50m/s. The magnitude of change in momentum of the body during its flight is ??

**Q.**In order to make the effective acceleration due to gravity equal to zero at the equator, the angular velocity of rotation of the earth about its axis should be (g=10 ms−2 and radius of earth is 6400 km)

**Q.**

Out of the following four dimensional quantities, which one qualifies to be called a dimensional constant?

Acceleration due to gravity

Surface tension of water

Weight of a standard kilogram mass

The velocity of light in vacuum

**Q.**

Derive an expression for acceleration due to gravity at a depth d below the earths earth surface.

**Q.**

If the mass of a body is $9.8kg$on earth, what is its mass on the moon?

**Q.**A simple pendulum has a time period T1 when on the earth's surface and T2 when taken to a height 2R above the earth's surface, where R is the radius of the earth. The value of (T1T2) is:

- 19
- 13
- √3
- 9

**Q.**If a man at the equator would weigh (35)th of his weight, the angular speed of the earth is

- √2R5g
- √2g5R
- √Rg
- √gR

**Q.**

The diameter and mass of a planet are double that of Earth. Then the time period of a pendulum at the surface of the planet is how much times of time period at Earths surface?

**Q.**

Where is acceleration due to gravity maximum?

**Q.**

The value of acceleration due to gravity ′g′, at the earths surface, is $10m/{s}^{2}$. Its value at the center of the earth which is assumed to be a sphere of radius ′R′ and uniform mass density is :

**Q.**

If the mass of the earth is $80$ times that of a planet and diameter is double that of a planet and $\mathrm{g}$ on the earth is $9.8{\mathrm{ms}}^{-2}$ , then the value of $\mathrm{g}$ on that planet is = ______ ${\mathrm{ms}}^{-2}$

$4.9$

$0.98$

$0.49$

$49$

**Q.**The change in the gravitational potential energy when a body of mass m is raised to a height nR above the surface of the earth is:

- nn−1(mgR)

- nmgR

- nn+1(mgR)

- (mgR)n

**Q.**

If earth stands still what will be its effect on man’s weight

Increases

Decreases

None of these

Remains same

**Q.**If the radius of the earth contracts to half of its present value without a change in its mass, then new duration of the day will be;

- 12 h
- 6 h
- 4 h
- 3 h