Two Equal Masses m and m are Hung From A Balance Whose Scale Pans Differ In Vertical Height By h. Calculate The Error In Weighing, If Any, In Terms Of Density Of Earth ρ.

A body is at a height equal to the radius of the earth from the surface of the earth. With what velocity be it thrown so that it goes out of the gravitational field of the earth? Given:

N m² kg^–2.

A particle falls on the surface of the earth from infinity. If the initial velocity of the particle is zero and friction due to air is negligible, find the velocity of the particle when it reaches the surface of the earth. Also find its kinetic energy. (Radius of earth is 6400 km and g is 9.8 m/s².)

A mass of  is to be compressed in the form of a sphere. The escape velocity from its surface is  What should be the radius of the sphere. Gravitational constant

Imagine a planet whose diameter and mass are both one-half of those of earth. The day’s surface temperature of this planet reaches upto 800 K. Are oxygen molecules possible in the atmosphere of this planet? Give calculation. (Escape velocity on earth’s surface = 11.2 km s^–1, Boltzmann’s constant

k = 1.38 × 10^–23 JK^–1, mass of oxygen molecule = 5.3 × 10^–26 kg.)

A hollow spher is made of a lead of radius R such that its surface touches the outside surface of the lead sphere and passes through its centre. The mass of the lead sphere before hollowing was M. What is the force of attraction that this sphere would exert on a particle of mass m which lies at a distance from the centre of the lead sphere on the straight line joining the centres of the sphere and the hollow (as shown in fig.)?

What are the values of gravitational attraction and potential at the surface of earth referred to zero potential at infinite distance? Given that the mass of the earth is  the radius of earth is 6400 km and G = 6.67 ×10 ^–11MKS units.

In a certain region of space gravitational field is given by I = – (K/r). Taking the reference point to be at r = r₀ with V = V₀, find the potential.

Calculate the acceleration due to gravity at the surface of Mars if its diameter is 6760 km and mass one-tenth that of earth. The diameter of earth is 12742 km and acceleration due to gravity on earth is 9.8 m/s².

Compute the mass and density of the moon if acceleration due to gravity on its surface is 1.62 m/s² and its radius is 

Three particles each of mass m are placed at the corners of an equilateral triangle of side d. Calculate (a) the potential energy of the system, (b) work done on this system if the side of the triangle is changed from d to 2d.