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Mechanics
Easy
Question
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
The correct answer is:
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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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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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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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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
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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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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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The distance of Neptune and Saturn from the Sun are respectively 
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meters and their periodic times are respectively 
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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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Let V and E denote the gravitational potential and gravitational field, respectively, at a point due to certain uniform mass distribution described in four different situations of Column I. Assume the gravitational potential at infinity to be zero. The values of E and V are given in Column II Match the statement in column I with the results in Column II.
|
Column I |
Column II |
| i. At the centre of thin spherical shell |
a. E = 0 |
| ii. At the centre of solid sphere |
b. E ≠ 0 |
| iii. A solid sphere has a non-concentric spherical cavity. At the centre of the spherical cavity |
c. V ≠ 0 |
| iv. At the centre of the joining two point masses of equal magnitude |
d. V = 0 |
Let V and E denote the gravitational potential and gravitational field, respectively, at a point due to certain uniform mass distribution described in four different situations of Column I. Assume the gravitational potential at infinity to be zero. The values of E and V are given in Column II Match the statement in column I with the results in Column II.
|
Column I |
Column II |
| i. At the centre of thin spherical shell |
a. E = 0 |
| ii. At the centre of solid sphere |
b. E ≠ 0 |
| iii. A solid sphere has a non-concentric spherical cavity. At the centre of the spherical cavity |
c. V ≠ 0 |
| iv. At the centre of the joining two point masses of equal magnitude |
d. V = 0 |
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A frictionless tunnel is dug along a chord of the earth of at a perpendicular distance R/2 from the centre of earth (where R is radius of earth). An object is released from one end of the tunnel.
Time period of oscillation of the object is
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A frictionless tunnel is dug along a chord of the earth of at a perpendicular distance R/2 from the centre of earth (where R is radius of earth). An object is released from one end of the tunnel.
Time period of oscillation of the object is
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A frictionless tunnel is dug along a chord of the earth of at a perpendicular distance R/2 from the centre of earth (where R is radius of earth). An object is released from one end of the tunnel.
The correct graph, showing the variation of magnitude of acceleration of object with its distance from centre of earth is
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The correct graph, showing the variation of magnitude of acceleration of object with its distance from centre of earth is
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Gravitational force is a conservative and medium independent force. Its nature is attractive. Gravitational field intensity and gravitational potential gives information about gravitational field in vector and scalar form respectively. Actually gravitational field intensity is equal to the negative of the potential gradient. Potential energy is defined for only conservative force. It is also equal the total energy in escaping condition. Gravitational potential is either negative or zero but can never be positive due to attractive nature of gravitational force, if potential at infinity is taken zero.
Gravitational potential V versus distance r graph is represented in figure. The magnitude of gravitational field intensity is equal to
Gravitational force is a conservative and medium independent force. Its nature is attractive. Gravitational field intensity and gravitational potential gives information about gravitational field in vector and scalar form respectively. Actually gravitational field intensity is equal to the negative of the potential gradient. Potential energy is defined for only conservative force. It is also equal the total energy in escaping condition. Gravitational potential is either negative or zero but can never be positive due to attractive nature of gravitational force, if potential at infinity is taken zero.
Gravitational potential V versus distance r graph is represented in figure. The magnitude of gravitational field intensity is equal to
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Gravitational force is a conservative and medium independent force. Its nature is attractive. Gravitational field intensity and gravitational potential gives information about gravitational field in vector and scalar form respectively. Actually gravitational field intensity is equal to the negative of the potential gradient. Potential energy is defined for only conservative force. It is also equal the total energy in escaping condition. Gravitational potential is either negative or zero but can never be positive due to attractive nature of gravitational force, if potential at infinity is taken zero.
A person brings a mass of 1 kg from infinity to a point A. Initially the mass was at rest but it moves with a speed of 2 m/s as it reaches A. The work done by the person on the mass is -3J. The potential of A is
Gravitational force is a conservative and medium independent force. Its nature is attractive. Gravitational field intensity and gravitational potential gives information about gravitational field in vector and scalar form respectively. Actually gravitational field intensity is equal to the negative of the potential gradient. Potential energy is defined for only conservative force. It is also equal the total energy in escaping condition. Gravitational potential is either negative or zero but can never be positive due to attractive nature of gravitational force, if potential at infinity is taken zero.
A person brings a mass of 1 kg from infinity to a point A. Initially the mass was at rest but it moves with a speed of 2 m/s as it reaches A. The work done by the person on the mass is -3J. The potential of A is
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The minimum and maximum distances of a satellite from the centre of the earth are 2R and 4R, respectively, where R is the radius of the earth and Mis the mass of the earth.
The radius of curvature at the point of minimum distance is
The minimum and maximum distances of a satellite from the centre of the earth are 2R and 4R, respectively, where R is the radius of the earth and Mis the mass of the earth.
The radius of curvature at the point of minimum distance is
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The minimum and maximum distances of a satellite from the centre of the earth are 2R and 4R, respectively, where R is the radius of the earth and Mis the mass of the earth.
The minimum and maximum speeds are
Paragraph
The minimum and maximum distances of a satellite from the centre of the earth are 2R and 4R, respectively, where R is the radius of the earth and Mis the mass of the earth.
The minimum and maximum speeds are
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