Variation of G Due to the Rotation of Earth

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

1. $\frac{r}{2}$
2. $\frac{r}{2\sqrt{2}}$
3. $\frac{r}{(4{)}^{1/3}}$
4. $\frac{r}{(2{)}^{1/3}}$

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 ${\left(\frac{1}{9}\right)}^{\text{th}}$ 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).

1. $\frac{R}{2}$
2. $\frac{R}{3}$
3. $\frac{R}{4}$
4. $\frac{R}{9}$

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:

1. $\frac{L}{m}$
2. $\frac{4L}{m}$
3. $\frac{L}{2m}$
4. $\frac{2L}{m}$

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:

1. $T^2\propto R$

2. $T^2\propto R^3$

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

4. $T\propto R$

Q.

The average density of the earth

1. The complex function of g

2. Does not depend on g

3. Inversely proportional to g

4. 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:

$$\begin{gathered} g=9.8m{s}^{-2} \\ R=6.38\times {10}^{6}m \\ G=6.67\times {10}^{-11}M.K.S.units. \end{gathered}$$

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 $2.45{\text{m/s}}^2$. The height of the spaceship from earth's surface is
$(R=$ radius of earth $)$

1. $3R$
2. $2R$
3. $R$
4. $R/2$

Q. A solid sphere of mass $M$ and radius $R$ has a spherical cavity of radius $\frac{R}{2}$ such that the centre of cavity is at a distance $\frac{R}{2}$ from the centre of the sphere. A point mass $m$ is placed inside the cavity at a distance $\frac{R}{4}$ from the centre of sphere. The gravitational force on mass $m$ is

1. $\frac{GMm}{R^2}$
2. $\frac{GMm}{2R^2}$
3. $\frac{2GMm}{R^2}$
4. $\frac{GMm}{4R^2}$

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 $Y{Y}^1$

1. 

2. 

3. 

4. 

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

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

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

3. $M{R}^2$

4. $\frac{M}{R}$

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 $(g=10m{s}^{-2}andradiusofearthis6400km)$

1. 
2. 
3. 
4. 

Q.

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

1. Acceleration due to gravity

2. Surface tension of water

3. Weight of a standard kilogram mass

4. 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 $T_1$ when on the earth's surface and $T_2$ when taken to a height $2R$ above the earth's surface, where $R$ is the radius of the earth. The value of $\left(\frac{T_1}{T_2}\right)$ is:

1. $\frac{1}{9}$
2. $\frac{1}{3}$
3. $\sqrt{3}$
4. $9$

Q. If a man at the equator would weigh ${\left(\frac{3}{5}\right)}^{th}$ of his weight, the angular speed of the earth is.

1. $\sqrt{\frac{2R}{5g}}$
2. $\sqrt{\frac{2g}{5R}}$
3. $\sqrt{\frac{R}{g}}$
4. $\sqrt{\frac{g}{R}}$

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 = ______ ${\mathrm{ms}}^{-2}$

1. $4.9$

2. $0.98$

3. $0.49$

4. $49$

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:

1. $\frac{n}{n-1}\left(mgR\right)$
   
2. $nmgR$
   
3. $\frac{n}{n+1}\left(mgR\right)$
   
4. $\frac{\left(mgR\right)}{n}$

Q.

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

1. Increases

2. Decreases

3. None of these

4. 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;

1. $12\text{h}$
2. $6\text{h}$
3. $4\text{h}$
4. $3\text{h}$