Newton's Law of Gravitation

Q.

A thin rod of mass M and length L is bent in semicircle as shown in figure. The gravitational force on a particle with mass m at O, the centre of curvature is...

1. 

2. zero

3. 

4. 

Q. When two displacements represented by y1=a sin(ω t) and y2 =b cos(ω t) are superimposed the motion is?

Q.

The period of a satellite in a circular orbit of radius R is T, the period of another satellite in a circular orbit of radius 4R is

1. 4T

2. 8T

3. T/4

4. T/8

Q. Two identical spheres are placed in contact with each other. The force of gravitation between the spheres will be proportional to (R = radius of each sphere)

1. $R$
2. $R^2$
3. $R^4$
4. $Noneofthese$

Q.

If the period of revolution of an artificial satellite just above the earths surface is T and the density of earth is $\rho$, then $\rho T^2$ is

1. 

2. 

3. Proportional to radius of earth R

4. Proportional to square of the radius of earth R² Here, G= universal gravitational constant

Q.

Gravitational mass is proportional to gravitational

1. Field

2. Force

3. Intensity

4. All of these

Q. At a metro station, a girl walks up a stationary escalator in time t1. If she remains stationary on the escalator, then the escalator take her up in time t2. The time taken by her to walk up on the moving escalator will be (a) (t1 + t2)/2 (c) t1t2/(t2+t1) (b) t1t2/(t2–t1) (d) t1–t2

Q.

The gravitational field due to a mass distribution is $E=\frac{K}{x^3}$ in the x - direction (K is a constant).Taking the gravitational potential to be zero at infinity, its value at a distance x is:

1. K / x

2. K / 2x

3. K / x 2

4. K / 2x²

Q.

The mass of the moon is about $1.2\%$ the mass of the earth. Compared to the gravitational force the earth exerts on the moon, the gravitational force the moon exerts on the earth

1. Is the same

2. Is smaller

3. Is greater

4. Varies with its phase

Q. 12. If radius of earth becomes n times its present value without change in mass then duration of day becomes

Q.

Infinite no.of bodies, each of mass 3kg are situated at distances 1m, 2m, 4m, 8m....... respectively on x-axis. The resultant intensity of gravitational field at the origin will be

1. G

2. 2G

3. 3G

4. 4G

Q.

A satellite moves in a circle around the earth. The radius of this circle is equal to one half the radius of the moons orbit. This satellite completes one revolution in

1. 

2. 

3. 

4. 

Q. A rocket is fired from the earth towards the sun. At what distance from the earth’s centre is the gravitational force on the rocket zero ? Mass of the sun = 2×10³⁰ kg, mass of the earth = 6×1024 kg. Neglect the effect of other planets etc. (orbital radius = 1.5 × 10¹¹ m).

Q. Answer the following : (a) You can shield a charge from electrical forces by putting it inside a hollow conductor. Can you shield a body from the gravitational influence of nearby matter by putting it inside a hollow sphere or by some other means ? (b) An astronaut inside a small space ship orbiting around the earth cannot detect gravity. If the space station orbiting around the earth has a large size, can he hope to detect gravity ? (c) If you compare the gravitational force on the earth due to the sun to that due to the moon, you would find that the Sun’s pull is greater than the moon’s pull. (you can check this yourself using the data available in the succeeding exercises). However, the tidal effect of the moon’s pull is greater than the tidal effect of sun. Why ?

Q. 38. The height at which the weight of a body become 1�16, its weight on the surface of earth (Radius=R) is

Q.

Two planets of equal mass orbit a much more massive star (figure). Planet $m_1$ moves in a circular orbit of radius $1\times {10}^8$ km with period 2 year. Planet $m_2$ moves in an elliptical orbit with closest distance $r_1=1\times {10}^8$ km and farthest distance $r_{2}1.8\times {10}^8$km, as shown. Using the fact that mean radius of an elliptical orbit is the length of the semi-major axis, find the period of $m_2^{{}^{\prime }}$ s orbit.

1. 3.31 year

2. 4.12 year

3. 5.24 year

4. 2.1 year

Q. A star 2.5 times the mass of the sun and collapsed to a size of 12 km rotates with a speed of 1.2 rev. per second. (Extremely compact stars of this kind are known as neutron stars. Certain stellar objects called pulsars belong to this category). Will an object placed on its equator remain stuck to its surface due to gravity ? (mass of the sun = 2×10³⁰ kg).

Q. The maximum vertical distance through which a fully dressed astronaut can jump on the earth is 0.7 m. Estimate the maximum vertical distance through which she can jump on a planet, which has a mean density (5/9) times that of earth and radius one quarter that of the earth.

Q.

A body of mass m is taken to the bottom of a deep mine. Then

1. Its mass increases

2. Its mass decreases

3. Its weight increases

4. Its weight decreases

Q.

A particle of mass m was transferred from the centre of the base of a uniform hemisphere of mass M and radius R to infinity. How much work would be performed in this process by the gravitational force exerted on the particle by the hemisphere?

1. 

2. 

3. 

4. 

Q.

Gravitational attraction on Earth on the stone of mass $M$ is$F_S$. If the force on the hydrogen balloon of mass $M$ located at the same space is $F_B$, then

1. $F_S>F_B$

2. $F_S<F_B$

3. $F_s=F_B$

4. $F_S=-F_B$

Q. (4) 621. At a railway station, a boy walks up a stationaryescalator in time 3 s. If he remains stationary on theescalator, then the escalator take him up in time 6 sThe time taken by him to walk up on the movingescalator is- SCoa1600+ d3(1) 9 sa= 666--2m(2) 2 s(3) 1s o(l06)(4) 4.5

Q.

Water rises in a capillarity tube to a height 2.0 cm. if the tube is inclined at an angle of 60° with the vertical, what will be the length of the water column within the tube?

1. cms

2. 1 cm

3. None of these

4. 4 cms

Q.

A sphere of mass M and radius R₂ has a concentric cavity of radius R_{1 as} shown in figure. The force F exerted by the sphere on a particle of mass m located at a distance r from the center of sphere varies as (0 $\le$ r $\le$ ∞)

1. 

2. 

3. 

4. 

Q.

A tunnel is dug along a chord of the earth at a perpendicular distance R/2 from the earth's centre. The wall of the tunnel may be assumed to be frictionless. A particle is released from one end of the tunnel. The pressing force by the particle on the wall and the acceleration of the particle varies with x (distance of the particle from the centre) according to

1. 

2. 

3. 

4. 

Q.

The interaction between earth and moon which keeps the moon revolving around the earth can be named as a ?

Q.

Two air bubbles in water

1. Attract each other

2. Repel each other

3. Do not exert any force on each other

4. May attract or repel depending upon the distance between them

Q. A satellite of mass $m$ revolves around earth of mass $M$ in a circular orbit of radius $r$ with angular velocity $\omega$. If radius of the orbit becomes $9r$, then angular velocity of the satellite in the new orbit will be

1. $9\omega$
2. $\frac{\omega }{27}$
3. $27\omega$
4. $\frac{\omega }{9}$

Q. What is the displacement of a body in n seconds?

Q.

A geostationary satellite orbits around the earth in a circular orbit of radius 36, 000 km. Then, the time period of a spy satellite orbiting a few hundred km above the earth's surface (Re = 6400 km) will approximately​

be:

1. 1/2 = h

2. 1 h

3. 2 h

4. 4 h