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Mechanics
Easy
Question
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 vary with x (distance of the particle from the centre of earth ) according to
The correct answers are: ,
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Physics
Figure shows the kinetic energy 
and potential energy 
curves for a two-particle system. Name the point at which the system is bound.
Figure shows the kinetic energy and potential energy curves for a two-particle system. Name the point at which the system is bound.
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A triple star system consists of two stars, each of mass m , in the same circular orbit about central star with mass
. The two outer stars always lie at opposite ends o fa diameter of their common circular orbit. The radius of the circular orbit is 
and the orbital period of each star is
The orbital velocity of each star is
A triple star system consists of two stars, each of mass m , in the same circular orbit about central star with mass . The two outer stars always lie at opposite ends o fa diameter of their common circular orbit. The radius of the circular orbit is and the orbital period of each star is
The orbital velocity of each star is
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Physics
A triple star system consists of two stars, each of mass m , in the same circular orbit about central star with mass . The two outer stars always lie at opposite ends o fa diameter of their common circular orbit. The radius of the circular orbit is and the orbital period of each star is 
The mass m of the outer star is
A triple star system consists of two stars, each of mass m , in the same circular orbit about central star with mass . The two outer stars always lie at opposite ends o fa diameter of their common circular orbit. The radius of the circular orbit is and the orbital period of each star is
The mass m of the outer star is
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Physics
In the graph shown, the PE of earth-satellite system is shown by solid line as a function of distance r (the separation between earth's centre and satellite). The total energy of the two objects which may or may not be bounded to earth are shown in figure by dotted lines
Based on the above information answer the following questions:
If object having total energy E1 having same PE curve as shown in figure, then
In the graph shown, the PE of earth-satellite system is shown by solid line as a function of distance r (the separation between earth's centre and satellite). The total energy of the two objects which may or may not be bounded to earth are shown in figure by dotted lines
Based on the above information answer the following questions:
If object having total energy E1 having same PE curve as shown in figure, then
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Physics
In the graph shown, the PE of earth-satellite system is shown by solid line as a function of distance r (the separation between earth's centre and satellite). The total energy of the two objects which may or may not be bounded to earth are shown in figure by dotted lines.
Based on the above information answer the following questions:
Mark the correct statement
In the graph shown, the PE of earth-satellite system is shown by solid line as a function of distance r (the separation between earth's centre and satellite). The total energy of the two objects which may or may not be bounded to earth are shown in figure by dotted lines.
Based on the above information answer the following questions:
Mark the correct statement
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A solid sphere of mass m radius r is placed inside a hollow thin spherical shell of mass M and radius R as shown in figure. A particle of mass m’ placed on the line joining the two centres at a distance x from the point of contact of the sphere and the shell. Find the magnitude of the resultant gravitational force on this particle due to the sphere and the shell if
A solid sphere of mass m radius r is placed inside a hollow thin spherical shell of mass M and radius R as shown in figure. A particle of mass m’ placed on the line joining the two centres at a distance x from the point of contact of the sphere and the shell. Find the magnitude of the resultant gravitational force on this particle due to the sphere and the shell if
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Physics
A solid sphere of mass m radius r is placed inside a hollow thin spherical shell of mass M and radius R as shown in figure. A particle of mass m’ placed on the line joining the two centres at a distance x from the point of contact of the sphere and the shell. Find the magnitude of the resultant gravitational force on this particle due to the sphere and the shell if
A solid sphere of mass m radius r is placed inside a hollow thin spherical shell of mass M and radius R as shown in figure. A particle of mass m’ placed on the line joining the two centres at a distance x from the point of contact of the sphere and the shell. Find the magnitude of the resultant gravitational force on this particle due to the sphere and the shell if
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Physics
The gravitational field due to a mass distribution is given by E . K I x3 in x — direction. Taking the 
in x- gravitational potential to be zero at infinity, its value at distance x is:
The gravitational field due to a mass distribution is given by E . K I x3 in x — direction. Taking the in x- gravitational potential to be zero at infinity, its value at distance x is:
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Physics
A point p lies on the axis of a fixed ring of mass and radius R, at a distance 2R from its centre O. A small particle starts from p and reaches O under gravitational attraction only. Its speed at O will be:
A point p lies on the axis of a fixed ring of mass and radius R, at a distance 2R from its centre O. A small particle starts from p and reaches O under gravitational attraction only. Its speed at O will be:
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Physics
Two rings having masses M and 2M, respectively, having same radius are placed coaxially as shown in figure.
If the Mass distribution on both the rings is non-uniform, then gravitational potential at point p is
Two rings having masses M and 2M, respectively, having same radius are placed coaxially as shown in figure.
If the Mass distribution on both the rings is non-uniform, then gravitational potential at point p is
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Two identical spheres each of radius R are placed with their centres at a distance nR, where n is integer greater than 2. The gravitational force between them will be proportional to
Two identical spheres each of radius R are placed with their centres at a distance nR, where n is integer greater than 2. The gravitational force between them will be proportional to
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Physics
Two spheres of masses m and M are situated in air and the gravitational force between them is F. The space between the masses is now filled with a liquid of specific gravity 3. The gravitational force will now be
Two spheres of masses m and M are situated in air and the gravitational force between them is F. The space between the masses is now filled with a liquid of specific gravity 3. The gravitational force will now be
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Physics
The period of moon’s rotation around the earth is nearly 29 days. If moon’s mass were 2 fold its present value and all other things remain unchanged, the period of moon’s rotation would be nearly (in days)
The period of moon’s rotation around the earth is nearly 29 days. If moon’s mass were 2 fold its present value and all other things remain unchanged, the period of moon’s rotation would be nearly (in days)
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Physics
The distance of Neptune and Saturn from the Sun are respectively 
and 
meters and their periodic times are respectively 
and 
If their orbits are circular, then the value of 
is
The distance of Neptune and Saturn from the Sun are respectively and meters and their periodic times are respectively and If their orbits are circular, then the value of is
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Physics
A satellite is revolving around the earth in a circular orbit of radius a with velocity . A particle is projected from the satellite in forward direction with relative velocity 
. During the subsequent motion of the particle, match the following:
Column I
Column II
i. Total energy of particle
a.
ii. Minimum distance of particle from the earth
b. 
iii. Maximum distance of particle from the earth
c. 
d. 2a
e. 2 a/3
f. a
|
Column I |
Column II |
| i. Total energy of particle |
a. |
| ii. Minimum distance of particle from the earth |
b. |
| iii. Maximum distance of particle from the earth |
c. |
| |
d. 2a |
| |
e. 2 a/3 |
| |
f. a |
A satellite is revolving around the earth in a circular orbit of radius a with velocity . A particle is projected from the satellite in forward direction with relative velocity . During the subsequent motion of the particle, match the following:
Column I
Column II
i. Total energy of particle
a.
ii. Minimum distance of particle from the earth
b.
iii. Maximum distance of particle from the earth
c.
d. 2a
e. 2 a/3
f. a
|
Column I |
Column II |
| i. Total energy of particle |
a. |
| ii. Minimum distance of particle from the earth |
b. |
| iii. Maximum distance of particle from the earth |
c. |
| |
d. 2a |
| |
e. 2 a/3 |
| |
f. a |
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