Gravitational Potential

Q. 40. A particle with total energy E is moving on a potential energy region U(x) motion of particle is restricted to the region when A)U(x)>E b)U(x)

Q. In a certain region of space gravitational field is given by I=-(K/r)(where r is the dist from a fixed point and K is cons†an t). Taking the referance point to be at r=r° with V=V°.Find the potential at a dis†an ce r

Q.

What is the dimensional formula for the universal constant of gravitation?

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Q.

Which of the following is the evidence to show that there must be a force acting on earth and directed towards the sun

1. Revolution of the earth round the sun

2. Apparent motion of sun round the earth

3. Deviation of the falling bodies towards east

4. Phenomenon of day and night

Q. The gravitational potential in a region is given by V = –(x2 + y2 + z2) J/kg, where x, y and z are in m. The gravitational field intensity at point (1, 1, 0) m is Options: Should have chosen Wrong

Q. a conservative force in a region given by F = A\X^3i an expression for potential energy in the region assuming the potential at infinity to be zero

Q.

The masses and radii of the earth and moon are $M_1,R_{1}and{M}_2,R_2$ respectively. Their centres are distance d apart. The minimum velocity with which a particle of mass m should be projected from a point midway between their centres so that it escapes to infinity is

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2. 

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Q. Which Force is used for revolution of earth around sun?

Q. The direction of the gravitational intensity at an arbitrary point P for hemispherical shell of uniform mass density is indicated by the arrow:

1. $d$
2. $e$
3. $f$
4. $g$

Q.

In some region, the gravitational field is zero. The gravitational potential in this region

1. Must be variable

2. Must be constant

3. Cannot be zero

4. Must be zero

Q.

The potential at the surface of a planet of mass M and radius R is assumed to be zero. Choose the most appropriate option

1. The potential at infinity is $\frac{GM}{R}$

2. The potential at the center of planet is $-\frac{GM}{R}$

3. Both (a) and (b) are correct

4. Both (a) and (b) are wrong

Q. Choose the correct answer from among the given ones:
The gravitational intensity at the center of a hemispherical shell of uniform mass density has the direction indicated by the arrow in the above figure.

1. $a$
2. $c$
3. $0$
4. $b$

Q.

A solid sphere of uniform density and radius 4 units is located with its centre at the origin O of coordinates. Two spheres of equal radii 1 unit with their centres at A(- 2, 0, 0) and B(2, 0, 0) respectively are taken out of the solid leaving behind spherical cavities as shown in figure. Then,

1. The gravitational force due to this object at the origin is zero

2. The gravitational force at the point B (2, 0, 0) is zero

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4. 

Q. 78 if gravitational field is given byE=-xi-2y^2j.when gravitational potential is zero at(0, 0), findpotentialat(2, 1).

Q. Consider two point masses m and 2m ata distance of 3m in a gravity free space. Find the maximum possible velocity v which can be given to 2m so that 2m and m revolve in a closed orbit due to their mutual gravitation force of attraction.

Q. Solve

35. Keplers third law says that the square of period of revolution (T) of a planet around the sun is proportional to third power of average distance r between the sun and the planet i.e. $T^2=K{r}^3.$ Here K is constant

If the mass of sun and planet are M and m respectively then as per Newtons law of gravitation force of attraction between them is
$$\begin{gathered} F=\frac{GMm}{r^2},hereGisgravitationalcons\tan t. \\ TherelationbetweenGandKisdescribedas \\ a)GMK=4{\mathrm{\pi }}^2\mathrm{b})\mathrm{K}=\mathrm{G} \\ \mathrm{c})\mathrm{K}=\frac{1}{\mathrm{G}}\mathrm{d})\mathrm{GK}=4{\mathrm{\pi }}^2 \end{gathered}$$

Q. The diagram showing the variation of gravitational potential of earth with distance from the centre of earth is

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2. 
3. 
4. 

Q.

The masses and radii of the earth and moon are $M_1,R_{1}and{M}_2,R_2$ respectively. Their centres are distance d apart. The minimum velocity with which a particle of mass m should be projected from a point midway between their centres so that it escapes to infinity is

1. $2\sqrt{\frac{G}{d}(M_1+M_2)}$

2. $2\sqrt{\frac{2G}{d}(M_1+M_2)}$

3. $2\sqrt{\frac{Gm}{d}(M_1+M_2)}$

4. $2\sqrt{\frac{Gm(M_1+M_2)}{d(R_1+R_2)}}$

Q. explainn 2nd property of gravitation