Variation of G Due to Height and Depth

Q. The acceleration due to gravity at a height $1km$ above the earth is the same as at a depth $d$ below the surface of earth. Then

1. $d=2km$
2. $d=\frac{1}{2}km$
3. $d=1km$
4. $d=\frac{3}{2}km$

Q. A body weighs 63 N on the surface of the earth. What is the gravitational force on it due to the earth at a height equal to half the radius of the earth ?

Q.

If the radius of the earth is $R$ then height $h$ at which value of $g$ becomes one-fourth is

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

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

3. $R$

4. $\frac{R}{8}$

Q. Choose the correct alternative : (a) Acceleration due to gravity increases/decreases with increasing altitude. (b) Acceleration due to gravity increases/decreases with increasing depth (assume the earth to be a sphere of uniform density). (c) Acceleration due to gravity is independent of mass of the earth/mass of the body. (d) The formula –G Mm(1/r₂ – 1/r₁) is more/less accurate than the formula mg(r₁– r₁) for the difference of potential energy between two points r₂ and r₁ distance away from the centre of the earth

Q. stration15.A solid sphere of uniform density and radius R exerts a gravitational force of attraction F, on a partiP, distant 2R from the centre of the sphere. A spherical cavity of radius R/2 is now formed in the sphereas shown in figure. The sphere with cavity now applies a gravitational force F2 on the same particle Pthe ratio F/F

Q. Assuming the earth to be a sphere of uniform mass density, how much would a body weigh half way down to the centre of the earth if it weighed 250 N on the surface ?

Q.

If $g$ is the acceleration due to gravity on the surface of the earth, its value at a height equal to double the radius of the earth is

1. $g$

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

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

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

Q.

A satellite is revolving round the earth with orbital speed $v_0$. If it stops suddenly, the speed with which it will strike the surface of earth would be

($v_e$= escape velocity of a particle on earths surface)

1. 

2. 

3. 

4. 

Q.

The time period of simple pendulum is T. When the length increases by 10 cm, its period is $T_1$. When the length is decreased by 10 cm, its period is $T_2$ .Then the relation between T, $T_1$ and $T_2$ is

1. 

2. 

3. 

4. 

Q.

Find the potential energy of the gravitational interaction of a mass point m and a thin uniform rod of mass m and length L if they are located along a straight line at a distance a from each other

1. 

2. 

3. 

4. -1

Q.

The ratio of acceleration due to gravity at the earths surface and at a height h from the earths surface is 4. Determine the value of h in terms of the radius of earth.

Q. Three equal masses of 1kg each are placed at the vertices of equillateral triangle of side1m then gravitational force on one of the masses due to other mass

Q.

The value of g at the earths surface is 10 $m{s}^{-2}$, the value of g at a height of 3 $R_E$ from the surface of earth is

1. $\frac{10}{9}m{s}^{-2}$

2. $\frac{5}{8}m{s}^{-2}$

3. $\frac{3}{8}m{s}^{-2}$

4. $\frac{10}{8}m{s}^{-2}$

Q. 18.A point mass when enters d depth below the earth’s surface such that the g reduces by 1% then what is the value of d ?

Q.

How far away from the surface of the earth, does the acceleration due to gravity will be reduced by $36\%$ of its value on the surface of the earth if the radius of the earth is $6400km$?

1. $1200km$

2. $1600km$

3. $1750km$

4. $2000km$

Q. A body falls from a height \(h\) on a horizontal surface and rebounds. Then it falls again and rebounds and so on. If the coefficient of restitution is \(\dfrac{1}{2}\), then the total distance travelled by the ball before coming to rest is (neglect air resistance)

Q. A metal ball of mass $2\text{kg}$ moving with speed of $36\text{kmph}$ is having a collision with a stationary ball of mass $2\text{kg}$. If after collision, both the balls move together, the loss in kinetic energy due to collision is:

1. $80\text{J}$
2. $40\text{J}$
3. $60\text{J}$
4. $160\text{J}$

Q. A body of mass $m$ thrown horizontally with velocity $v$, from the top of a tower of height $h$ touches the level ground at a distance of $250\text{m}$ from the foot of the tower. A body of mass $2m$ thrown horizontally with velocity $\frac{v}{2}$ from the top of a tower of height $4h$ will touch the level ground at a distance $x$ from the foot of tower. The value of $x$ is

1. $500\text{m}$
2. $250\text{m}$
3. $250\sqrt{2}\text{m}$
4. $125\text{m}$

Q.

The height of the point vertically above the earth’s surface, at which acceleration due to gravity becomes $1\%$ of its value at the surface is (Radius of the earth = R)

1. 8 R

2. 9 R

3. 10 R

4. 20 R

Q. A body of mass $2\text{kg}$ moving with a velocity $3\text{m/s}$ collides with a body of mass $1\text{kg}$ moving with a velocity of $4\text{m/s}$ in opposite direction. If the collision is head on and completely inelastic, then

1. Both particles move together with velocity $\left(\frac{2}{3}\right)\text{m/s}$
2. The momentum of system is $2\text{kg m/s}$ throughout
3. The momentum of system is $10\text{kg m/s}$
4. The loss of KE of system is $\left(\frac{49}{3}\right)J$

Q. ring of mass m and radius R is pivoted at a point on its periphery. It oscillates with time period T. If a point mass m is gently attached at lowest point, then new time period is

Q. Why net acceleration is greater than gravity when a body is going upward in presence of air resis†an ce

Q. A wooden ball of density $\sigma$ is released from the bottom of a tank which is filled with a liquid of density $\rho (\rho >\sigma )$ up to a height $h_1$. The ball rises in the liquid , emerges from its surface and attains a height $h_2$ in air. If viscous effects are neglected, the ratio $\frac{h_2}{h_1}$ is

1. $(\frac{\rho }{\sigma }+1)$
2. $\frac{\sigma }{\rho }$
3. $(\frac{\rho }{\sigma }-1)$
4. $\frac{\rho }{\sigma }$

Q.

what are the factors needed to hold atmosphere of the earth

Q. what is gravitational field strength inside a spherical shell??

Q. two bodies Aand B having masses Mand 3Mrespectively are kept at adistance 2.73 m apart. a small particle of mass m is to be placed so that the net gravitational force on it is zero. what will be its distance from body A

Q. difference between accleration and accleration due to gravity

Q. Solve this:

Q64. A solid sphere of mass M and radius R has a spherical cavity of radius R/2 such that the centre of cavity is at a distance R/2 from the centre of the sphere. A point mass m is placed inside the cavity at a distance R/4 from the centre of sphere. The gravitational force on mass m is

$$\begin{gathered} \left(\mathrm{a}\right)\frac{11\mathrm{GMm}}{{\mathrm{R}}^2}\left(\mathrm{b}\right)\frac{14\mathrm{GMm}}{{\mathrm{R}}^2} \\ \left(\mathrm{c}\right)\frac{\mathrm{GMm}}{2{\mathrm{R}}^2}\left(\mathrm{d}\right)\frac{\mathrm{GMm}}{{\mathrm{R}}^2} \end{gathered}$$

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. Two parallel glass plates are dipped partly in a liquid of density ${}^{\prime }{d}^{\prime }$ keeping them vertical. If the distance between the plates is ${}^{\prime }{x}^{\prime }$, surface tension for the liquid is $T$ and angle of contact is $\theta$, then rise of liquid between the plates due to capillary action will be:

1. $\frac{T\cos \theta }{xdg}$
2. $\frac{2T}{xdg\cos \theta }$
3. $\frac{2T\cos \theta }{xdg}$
4. $\frac{T\cos \theta }{xd}$