Assuming the earth to be a sphere of uniform mass density, how much would a body weigh half way down to the centre of the earth if it weighed 250 N on the surface?

A satellite orbits the earth at a height of 400 km above the surface. How much energy must be expended to rocket the satellite out of the earth’s gravitational influence? Mass of the satellite = 200 kg, mass of the earth = 6.0 xx10^24 kg, radius of the earth = 6.4 xx10^6 m, G = 6.67 x 10^-11 N m^2 kg ^-2 .

A black hole is a body from whose surface nothing may ever escape. What is the condition for a uniform spherical mass M to be a black hole? What should be the radius of such a black hole if its mass is the same as that of the Earth?

A body weighs 63 N on the surface of the earth. What is the gravitational force on it due to the earth at a height equal to half the radius of the earth?

Give the location of the centre of mass of a (i) sphere, (ii) cylinder, (iii) ring, and (iv) cube, each of uniform mass density. Does the centre of mass of a body necessarily lie inside the body?

A man of mass 70 kg stands on a weighing scale in a lift which is moving (a) upwards with a uniform speed of 10 m s^1 (b) downwards with a uniform acceleration of 5 m s^2, upwards with a uniform acceleration of 5 m s-^1z. What would be the readings on the scale in each case? What would be the reading if the lift mechanism failed and it hurtled down freely under gravity?

The elephant weighs 20,000 N stands on one foot of area 1000 cm2. How much pressure would it exert on the ground?

How will you ‘weigh the sun', that is estimate its mass? The mean orbital radius of the earth around the sun is 1.5 xx10^8 km.

A hoop of radius 2 m weighs 100 kg. It rolls along a horizontal floor so.that its centre of mass has a speed of 20 cm/s. How much work has to be done to stop it?