Newton's Law of Gravitation

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. The variation of acceleration due to gravity $g$ with distance $d$ from the centre of the earth is best represented by ($R$ = Earth's radius)

1. 
2. 
3. 
4. 

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. 

2. 

3. 

4. 

Q. At what height from the surface of earth, the gravitational potential and the value of g are $-5.4\times {10}^{7}J/k{g}^2$ and $6m/s^2$ respectively [take the radius of earth as 6400 km]

1. 1400 km
2. 2000 km
3. 1600 km
4. 2600 km

Q.

How do you find time with gravity and height?

Q.

Why does a body weigh more at the poles than at the equator?

Q.

Differentiate between gravitational constant($G$) and acceleration due to gravity($g$)

Q.

If the density of the earth is doubled keeping its radius constant then the acceleration due to gravity ( present value 9.8m/s²) will be

1. $2.45$ m/s²

2. $4.9$m/s²

3. $9.8$m/s²

4. $19.6$ mls²

Q.

The depth at which the effective value of acceleration due to gravity is $\frac{g}{4}$ is (R = radius of the earth)

1. 

2. 

3. 

4. 

Q.

The depth d at which the value of acceleration due to gravity becomes 1/n times the value at the surface, is [R = radius of the earth]

1. 

2. 

3. 

4. 

Q. If the unit of force is $100$ N, unit of length is $10$ m and unit of time is $100$ s, what is the unit of mass in this system of units?

Q. Minimum and maximum distance of a satellite from the center of earth are $2R$ and $4R$ respectively where $R$ is radius of earth. Radius of curvature at the point when satellite is at a distance $2R$ is $nR$, here $n$ is(Answer upto two decimal places)

Q.

The moon has no atmosphere, and acceleration due to gravity at its surface is one-sixth of that at earths surface. When a pendulum is taken from the earth to the moon, its time period will:

1. increase

2. decrease

3. unaffected

4. infinity

Q. If area $\left(A\right)$ velocity $\left(v\right)$ and density $\left(\rho \right)$ are base units, then the dimensional formula of force can be represented as:

1. $A^{2}v\rho$
2. $Av{\rho }^2$
3. $A{v}^2\rho$
4. $Av\rho$

Q. Mass particles of $1\text{kg}$ 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. Let $E$ be the energy required to raise a satellite to height $h$ above earth's surface and $E^{\prime }$ be the energy required to put the same satellite into orbit at that height. Then $\frac{E}{E^{{}^{\prime }}}$ is equal to

1. $\frac{2h}{(R+2h)}$
   
2. $\frac{2h}{(2R+3h)}$
   
3. $\frac{R}{(R+h)}$
   
4. $\frac{R}{(2h+R)}$
   

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. 
2. 
3. 
4. 

Q. If on heating liquid through ${80}^{\circ }C$, the mass expelled is $(\frac{1}{100}{)}^{th}$ of mass still remaining, the coefficient of apparent expansion of liquid is

1. $1.25\times {10}^{-4}{/}^{\circ }C$
2. None of these
3. $1.25\times {10}^{-5}{/}^{\circ }C$
4. $12.5\times {10}^{-4}{/}^{\circ }C$

Q.

Why is Newtons law of gravitation called inverse square law?

Q. The centripetal force acting on a satellite orbiting round the earth and the gravitational force of earth acting on the satellite both are equal to F. The net force on the satellite is

1. F
2. 2 F
3. 
4. Zero

Q.

Is gravity the opposite of entropy

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

Q.

What is the difference between the gravitational force and the force of gravity?

Q. The earth $(\text{mass}=6\times {10}^{24}\text{kg})$ revolves around the sun with an angular velocity of $2\times {10}^{-7}\text{rad/s}$ in a circular orbit of radius $1.5\times {10}^8\text{km}$. The force exerted by the sun on the earth (in Newtons) is

1. $36\times {10}^{21}$
2. $27\times {10}^{39}$
3. Zero
4. $18\times {10}^{25}$

Q.

A semicircular wire has a length L and mass M A particle of mass m is placed at the centre of the circle.
Find the gravitational attraction on the particle due to the wire.

Q.

Three identical point masses, each of mass 1 kg lie in the x-y plane at points (0, 0, 0), (0, 0.2m) and (0.2m, 0). The net gravitational force on the mass at the origin is

1. $1.67\times {10}^{-9}(\hat{i}+\hat{j})N$

2. $3.34\times {10}^{-10}(\hat{i}+\hat{j})N$

3. $1.67\times {10}^{-19}(\hat{i}+\hat{j})N$

4. $3.34\times {10}^{-10}(\hat{i}+\hat{j})N$

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. 

2. 

3. 

4. 

Q. Let $V_G$ and $E_G$ denote the gravitational potential and field respectively in a region, then choose the wrong statement.

1. $V_G=0,E_G=0$
2. $V_G\ne 0,E_G=0$
3. $V_G=0,E_G\ne 0$
4. $V_G\ne 0,E_G\ne 0$

Q. A wire ring of diameter $14cm$ is gently lowered on to a liquid surface and then pulled up. When the film just breaks, the force required is $0.0616N$. The surface tension of the liquid is

1. $70N/m$
2. $70dyne/cm$
3. None of these
4. $70N/m$

Q. An $\propto$ particle is situated in an electric field of ${10}^{6}N/C$. The force exerted on it is

1. $6.4\times {10}^{-3}N$
2. $3.2\times {10}^{-13}N$
3. $32\times {10}^{-13}N$
4. $64\times {10}^{-13}N$