Newton's Law of Gravitation

Q.

The tidal waves in the sea are primarily due to

1. The gravitational effect of the moon on the earth

2. The gravitational effect of the sun on the earth

3. The gravitational effect of venus on the earth

4. The atmospheric effect of the earth itself

Q. Two blocks of masses $3m$ and $2m$ are in contact on a smooth table. A force $P$ is first applied horizontally on block of mass $3m$ and then on mass $2m$. The contact forces between the two blocks in the two cases are in the ratio

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

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.

Two stars, each of mass m and radius R, are approaching each other for a head-on collision. They start approaching each other when their separation is r >> R. If their speed at this separation is negligible, the speed with which they collide would be

1. $v=\sqrt{Gm(\frac{1}{R}-\frac{1}{r})}$

2. $v=\sqrt{Gm(\frac{1}{2R}-\frac{1}{r})}$

3. $v=\sqrt{Gm(\frac{1}{R}+\frac{1}{r})}$

4. $v=\sqrt{Gm(\frac{1}{2R}+\frac{1}{r})}$

Q. Six point charges are placed at the vertices of a hexagon of side $1\text{m}$ as shown in figure.


What will be the force experienced by a charge $+q$ placed at centre of hexagon ?

1. $6k{q}^2$
2. Zero
3. $3k{q}^2$
4. $4k{q}^2$

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. In the figure shown below, which of the following is true?

1. a x A1 = b x A2
2. b x A1 = a x A2
3. A1 = A2
4. A1 = 2 x A2

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. Which of the following is true for the given cases?

1. E1 = 2 x E2
2. E2 = 2 x E1
3. E1 = E2
4. E1 = 4 x E2

Q. Two astronauts are floating in gravitational free space after having lost contact with their spaceship. The two will

1. move towards each other.
2. move away from each other.
3. will become stationary.
4. keep floating at the same distance between them.

Q. A mass M is split into two parts, m and (M–m), which are then separated by a certain distance. What ratio of m/M maximizes the gravitational force between the two parts

1. $\frac{1}{3}$
2. $\frac{1}{2}$
3. $\frac{1}{4}$
4. $\frac{1}{5}$

Q.

The Gauss' theorem for gravitational field may be written as

1. $\oint \overrightarrow{g}.\overrightarrow{d}S$ = $\frac{m}{G}$

2. -$\oint \overrightarrow{g}.\overrightarrow{d}s$ = 4$\pi$Gm

3. $\oint \overrightarrow{g}.\overrightarrow{d}s$ = $\frac{m}{4\pi G}$

4. -$\oint \overrightarrow{g}.\overrightarrow{d}s$ = $\frac{m}{G}$

Q.

Two particles of equal mass go round a circle of radius R under the action of their mutual gravitational attraction. The speed of each particle is

1. $v=\frac{1}{2R}\sqrt{\frac{1}{Gm}}$

2. $v=\sqrt{\frac{Gm}{2R}}$

3. $v=\frac{1}{2}\sqrt{\frac{Gm}{R}}$

4. $v=\sqrt{\frac{4Gm}{R}}$

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. $\frac{1}{2}=h$

2. 1 h

3. 2 h

4. 4 h

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. $\frac{K}{x}$

2. $\frac{K}{2x}$

3. $\frac{K}{x2}$

4. $\frac{K}{2x^2}$

Q.

A uniform solid sphere of mass M and radius a is surrounded symmetrically by a uniform thin spherical shell of equal mass and radius 2 a. the ratio of gravitational field at a distance $\frac{3}{2}$ a froth the centre to $\frac{5}{2}$ a from the centre is..

1. $\frac{25}{18}$

2. $\frac{16}{19}$

3. $\frac{25}{9}$

4. 1

Q.

Three particles, each of mass m, are placed at the vertices of an equilateral triangle of side a. The gravitational field intensity at the centroid of the triangle is

1. zero

2. $\frac{G{m}^2}{a^2}$

3. $\frac{2G{m}^2}{a^2}$

4. $\frac{3G{m}^2}{a^2}$

Q. The Earth rotates around the Sun and the required centric petal force is provided by

1. The gravitational attraction between the sun and the moon
2. The gravitational attraction between the sun and the earth
3. The gravitational attraction between the earth and the moon
4. The gravitational repulsion between the earth and the sun

Q.

Acceleration due to gravity __________ with depth below the surface of the earth.

Q. Which of the following is false about the gravitational force between the sun and the earth

1. It is proportional to the mass of the earth
2. It is proportional to the mass of the sun
3. It is inversely proportional to the distance between sun and earth
4. It is inversely proportional to the square of distance between sun and earth

Q. The square of the time period is proportional to the ___ power of the semi major axis of the ellipse

1. 2nd
2. 3rd
3. 4th
4. 5th

Q.

Imagine a light planet revolving around a very massive star in a circular orbit of radius R with a period of revolution T. If the gravitational force of attraction between the planet and the star is proportional to $R^{\frac{-5}{2}}$, and $T^2$ is proportional to

1. $R^3$

2. $R^{\frac{7}{2}}$

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

4. $R^{\frac{9}{2}}$

Q.

A straight rod of length L extends form x=a to x=L+a. The gravitational force on a point mass m at x=0 if the mass per unit length of the rod is (A+B$x^2$), is

1. $GmA(\frac{1}{a+L}-\frac{1}{a}+BL]$

2. $GmA[\frac{1}{a}-\frac{1}{a+L}+BL]$

3. $GmA\left[\right(\frac{1}{a+L}-\frac{1}{a})-BL]$

4. $GmA\left[\right(\frac{1}{a}-\frac{1}{a+L})-BL]$

Q. Particles of mass $1\text{kg}$ each are placed along $x-$ axis at $x=1,2,4,8,.....\infty$. Then gravitational force on a mass of $3\text{kg}$ placed at origin is ($G=$ universal gravitational constant)

1. $4\text{G}$
2. $\frac{4G}{3}$
3. $2\text{G}$
4. $\infty$

Q.

If the radius of earth contracts $\frac{1}{n}$ of its present value, the length of the day will be approximately

1. $\frac{24}{n}h$

2. $\frac{24}{n^2}h$

3. $24nh$

4. $24n^{2}h$

Q.

A body released from a height h takes time t to reach earth’s surface. The time taken by the same body released from the same height to reach the moon’s surface is

1. $t$

2. $6t$

3. $\sqrt{6}t$

4. $\frac{t}{6}$

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. $\frac{K}{x}$

2. $\frac{K}{2x}$

3. $\frac{K}{x2}$

4. $\frac{K}{2x^2}$

Q.

A uniform solid sphere of mass M and radius a is surrounded symmetrically by a uniform thin spherical shell of equal mass and radius 2 a. the ratio of gravitational field at a distance $\frac{3}{2}$ a froth the centre to $\frac{5}{2}$ a from the centre is..

1. $\frac{25}{18}$

2. $\frac{16}{19}$

3. $\frac{25}{9}$

4. 1

Q. Find the gravitational force of interaction between the mass $m$ and an infinite rod of varying mass density $\lambda$ such that $\lambda \left(x\right)=\lambda /x$, where $x$ is the distance from mass $m$. Given that mass $m$ is placed at a distance $d$ from the end of the rod on its axis as shown in figure.

1. $\frac{Gm\lambda }{d^2}$
2. $\frac{Gm\lambda }{2d^2}$
3. $\frac{Gm\lambda }{3d^2}$
4. $\frac{3Gm\lambda }{2d^2}$

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