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Mechanics
Easy
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If a body is released from a point at a height equal to n times the radius of the earth, its velocity on reaching the surface of the earth is N ( R is radius of earth)
The correct answer is:
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Physics
The gravitational field due to a mass distribution is given by 
in X - direction. Taking the gravitational potential to be zero at infinity, find its value at a distance 
.
The gravitational field due to a mass distribution is given by in X - direction. Taking the gravitational potential to be zero at infinity, find its value at a distance .
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The gravitational field in a region is given by the equation 
. If a particle of mass 2kg is moved from the origin to the point (12m,5m) in this region, the change in the gravitational potential energy is
The gravitational field in a region is given by the equation . If a particle of mass 2kg is moved from the origin to the point (12m,5m) in this region, the change in the gravitational potential energy is
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A particle is placed in a field characterized by a value of gravitational potential given by 
, where 'k' is a constant . If 
is the gravitational field then
A particle is placed in a field characterized by a value of gravitational potential given by , where 'k' is a constant . If is the gravitational field then
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The centres of ring of mass m and a sphere of mass M of equal radius R, are at a distance 
R apart as shown in fig. The force of attraction between the ring and the sphere is
The centres of ring of mass m and a sphere of mass M of equal radius R, are at a distance R apart as shown in fig. The force of attraction between the ring and the sphere is
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A spherically symmetric gravitational system of particle has a mass density 
where 
is a constant . A test mass can undergo circular motion under the influence of the gravitational field of particles. Its speed v as function of distance r from the centre of the system is represented by
A spherically symmetric gravitational system of particle has a mass density where is a constant . A test mass can undergo circular motion under the influence of the gravitational field of particles. Its speed v as function of distance r from the centre of the system is represented by
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Two uniform solid spheres of equal radii R , but mass M and 4M have a centre to centre separation 6R, as shown in Fig. The two spheres are held fixed A projectile of mass 'm' is projected from the surface of the sphere of mass M directly towards the centre of the second sphere .Obtain an expression for the minimum speed 'v' of the projectile so that it reaches the surface of the second sphere.
Two uniform solid spheres of equal radii R , but mass M and 4M have a centre to centre separation 6R, as shown in Fig. The two spheres are held fixed A projectile of mass 'm' is projected from the surface of the sphere of mass M directly towards the centre of the second sphere .Obtain an expression for the minimum speed 'v' of the projectile so that it reaches the surface of the second sphere.
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Kepler's third law states that square of period of revolution(T) of a planet around the sun, is proportional to third power of average distance r between sun and planet i.e.
here K is constant. If the masses of sun and planet are M and m respectively then as for Newton's law of gravitation force of attraction between them is 
, here G is gravitational constant. The relation between G and K is described as
Kepler's third law states that square of period of revolution(T) of a planet around the sun, is proportional to third power of average distance r between sun and planet i.e. here K is constant. If the masses of sun and planet are M and m respectively then as for Newton's law of gravitation force of attraction between them is , here G is gravitational constant. The relation between G and K is described as
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Two particles of mass 'm' and '2m' are at a distance '3r' apart at the ends of a straight line AB. C is the centre of mass of the system. The magnitude of the gravitational force on a unit mass placed at C due to the masses is
Two particles of mass 'm' and '2m' are at a distance '3r' apart at the ends of a straight line AB. C is the centre of mass of the system. The magnitude of the gravitational force on a unit mass placed at C due to the masses is
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Imagine a light planet revolving around a massive star in circular orbit of radius R with a period of revolution T. If the gravitational force or attraction between the planet and the star is proportional to R-5/2 then T2 is proportional to
Imagine a light planet revolving around a massive star in circular orbit of radius R with a period of revolution T. If the gravitational force or attraction between the planet and the star is proportional to R-5/2 then T2 is proportional to
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A mass M is split into two parts m and (M-m) and then they are separated by a certain distance. If the gravitational force between them is to be maximum.
A mass M is split into two parts m and (M-m) and then they are separated by a certain distance. If the gravitational force between them is to be maximum.
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The gravitational force acting on a particle, due to a solid sphere of uniform density and radius R , at a distance of 3R from the center of the sphere is F1. A spherical hole of radius (R/2) is now made in the sphere as shown in the figure. The sphere with hole now exerts a force F2, on the same particle .Ratio F1,to F2 is
The gravitational force acting on a particle, due to a solid sphere of uniform density and radius R , at a distance of 3R from the center of the sphere is F1. A spherical hole of radius (R/2) is now made in the sphere as shown in the figure. The sphere with hole now exerts a force F2, on the same particle .Ratio F1,to F2 is
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A particle of mass m is situated at a distance d from one end of a rod of mass M and length L as shown in fig. Find the magnitude of the gravitational force between them.
A particle of mass m is situated at a distance d from one end of a rod of mass M and length L as shown in fig. Find the magnitude of the gravitational force between them.
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Two lead balls of masses m and 5m and radii R and 2R are separated by 12R. If they attract each other by gravitational force, the distance covered by small sphere before they touch each other is
Two lead balls of masses m and 5m and radii R and 2R are separated by 12R. If they attract each other by gravitational force, the distance covered by small sphere before they touch each other is
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Three uniform spheres each of mass 'm' and diameter D are kept in such a way that each touches the other two, then magnitude of the gravitational force on any one sphere due to the other two is
Three uniform spheres each of mass 'm' and diameter D are kept in such a way that each touches the other two, then magnitude of the gravitational force on any one sphere due to the other two is
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Physics
An infinite number of particles each of mass m are placed on the positive X—axis a 
from the origin. Find the magnitude of the resultant gravitational force on mass 'm' kept at the origin..
An infinite number of particles each of mass m are placed on the positive X—axis a from the origin. Find the magnitude of the resultant gravitational force on mass 'm' kept at the origin..
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