Variation of g (Acceleration Due to Gravity)

Q.

Calculate mass of the Earth from given data, Acceleration due to gravity $g=9.81m/s^2$, Radius of the Earth $R_e=6.37\times {10}^{6}m$, $G=6.67\times {10}^{-11}N{m}^2/k{g}^2$

Q.

Why is the value of acceleration due to gravity zero at the center of the Earth? Prove with mathematical calculations.

Q.

The masses and radii of the earth and moon are$M_1$, $R_1$ and $M_2$, $R_2$ respectively. Their centres are a distance d apart. The minimum speed with which a particle of mass m should be projected from a point midway between the two centres so as to escape to infinity is given by

1. $2{\left[\frac{G(M_1+M_2)}{md}\right]}^{\frac{1}{2}}$

2. $2{\left[\frac{G(M_1+M_2)}{d}\right]}^{\frac{1}{2}}$

3. $2{\left[\frac{G(M_1-M_2)}{md}\right]}^{\frac{1}{2}}$

4. $2{\left[\frac{G(M_1-M_2)}{d}\right]}^{\frac{1}{2}}$

Q.

A box weighs$196N$ on a spring balance at the North Pole. Its weight recorded on the same balance if it is shifted to the equator is close to (Take $g=10m/s^2$ at the North Pole and radius of the Earth $R_e=6400km$)

1. $194.32N$

2. $194.66N$

3. $195.34N$

4. $195.66N$

Q. Question 8
The value of quantity G in the law of gravitation

(a) depends on mass of earth only
(b) depends on radius of earth only
(c) depends on both mass and radius of earth
(d) is independent of mass and radius of the earth

Q.

Determine the value and units of universal Gravitational constant, G.

Q.

At which of the following locations, the value of g is the largest ?

1. Far above the surface of Earth

2. At the surface of Earth

3. Below the surface of Earth

4. At the centre of Earth

Q.

Assuming earth to be a solid sphere of uniform density $5800kg{m}^{-3}$and radius $6\times {10}^{6}m$, calculate the value of ‘g’ on its surface.

Q. The masses of two planets are in the ratio 1:2. Their radii are in the ratio 1:2. The acceleration due to gravity on the planets are in the ratio:

1. 3:5
2. 5:3
3. 2:1
4. 1:2

Q.

The radius of earth is 6400 km. What is its mass?

1. $6.0\times {10}^{24}$kg

2. $5.0\times {10}^{24}$kg

3. $1.0\times {10}^{22}$kg

4. $6.5\times {10}^{14}$kg

Q.

Force of gravity is least at the_______.

1. The equator

2. A point in between equator and any pole

3. The poles

4. None of these

Q.

A hypothetical planet has density r, radius R and surface gravitational acceleration g. If the radius of the planet were doubled, but the planetary density stayed the same, the acceleration due to gravity at the planet’s surface would be:

1. 4g

2. 2g

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

4. g

Q.

The masses and radii of the earth and moon are$M_1$, $R_1$ and $M_2$, $R_2$ respectively. Their centres are a distance d apart. The minimum speed with which a particle of mass m should be projected from a point midway between the two centres so as to escape to infinity is given by

1. $2{\left[\frac{G(M_1-M_2)}{d}\right]}^{\frac{1}{2}}$

2. $2{\left[\frac{G(M_1+M_2)}{md}\right]}^{\frac{1}{2}}$

3. $2{\left[\frac{G(M_1+M_2)}{d}\right]}^{\frac{1}{2}}$

4. $2{\left[\frac{G(M_1-M_2)}{md}\right]}^{\frac{1}{2}}$

Q.

State whether the following statement is true or false.

Value of “ g ” on the surface of the earth is $9.8{\text{ms}}^{-2}$

1. True
2. False

Q.

If g is the acceleration due to gravity on the surface of the earth, it's value at a height equal to triple the radius of earth is (assuming the earth to be a perfect sphere)

Q.

The average value of acceleration due to gravity at sea level is ___ $m{s}^{-2}$.

Q.

The average value of $g$on the surface of the earth is ___ .

Q. The value of g remains the same at all the places on the earths surface. Is this statement true?

Q.

Differentiate between $g$and $\mathrm{G}$.

Q. Question 25
Two objects of masses $m_1$ and $m_2$ having the same size are dropped simultaneously from heights $h_1$ and $h_2$ respectively. Find out the ratio of time they would take in reaching the ground. Will this ratio remain the same if (i) one of the objects is hollow and the other one is solid and (ii) both of them are hollow, size remaining the same in each case. Give reason.

Q. A spherical planet has a mass $M_p$. and diameter $D_p$. A particle of mass m falling freely near the surface of this planet will experience an acceleration due to gravity, equal to

1. $\frac{4G{M}_p}{D_p^2}$
2. $\frac{G{M}_{p}m}{D_p^2}$
3. $\frac{G{M}_p}{D_p^2}$
4. $\frac{4G{M}_{p}m}{D_p^2}$

Q. (a) Assuming the earth to be a sphere of uniform density, calculate the value of acceleration due to gravity at a point (i) $1600$km above the earth, (ii) $1600$km below the earth, (b) Also find the rate of variation of acceleration due to gravity above and below the earth's surface. Radius of earth $=6400$km, $g=9.8m/s^2$.

Q. If the distance between earth and sun is increased by $2$%, then find percentage change in gravitational force acting between them.

Q.

The acceleration due to gravity is zero at:

1. the equator

2. poles

3. sea level

4. the centre of the earth

Q. If the value of g at the surface of the earth is $9.8m{s}^{-2}$, then the value of g at a place $480$ km above the surface of the earth will be (radius of earth$=6400km$)

1. $4.2m{s}^{-2}$
2. $7.2m{s}^{-2}$
3. $8.5m{s}^{-2}$
4. $9.8m{s}^{-2}$

Q.

Consider a particle of mass m suspended vertically by a string at the equator. Let R and M denote the radius and the mass of the earth respectively. If $\omega$ is the angular velocity of earth's rotation about its own axis, the tension in the string is equal to

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

2. $\frac{GmM}{R^2}+m{\omega }^{2}R$

3. $\frac{GmM}{2R^2}$

4. $\frac{GmM}{R^2}-m{\omega }^{2}R$

Q. If the radius of earth were to shrink by one percent, its mass remaining the same, the acceleration due to gravity on the earths surface would

1. decrease
2. remains unchanged
3. increase.
4. none of these

Q. If the gravitational force were to vary inversely as $m^{th}$ power of the distance, then the time period of a planet in circular orbit of radius r around the sun will be proportional to

1. $r^{-m/2}$
2. $r^{m/2}$
3. $r^m$
4. $r^{\left(\frac{m+1}{2}\right)}$

Q. The value of acceleration due to gravity at the surface of all planets is the same.

1. True
2. False

Q. If the radius of the earth shrinks by $4\%$ and there is no change in its mass then by how much does the value of $g$ change?
( Given for $x<<1$ , assume $\frac{1}{(1-x{)}^2}\approx 1+2x$)

1. $2\%$
2. $4\%$
3. $16\%$
4. $8\%$