Gravitation Tes...

A spring balance is calibrated at sea level. If this balance is used to measure the weight of a body at successive increasing heights from the surface of the earth, then the weight indicated by spring balance will

An object lying at the equator of the earth will fly off the surface (will feel weightlessness), if the length of the day becomes

At a height $$h$$ above the surface of earth, the change in value of $$g$$ is same as that at a depth $$x$$ below the surface on the earth. Both $$x$$ and $$h$$ are very small in comparison to the radius of the earth. Then,

If the change in the value of $$g$$ at height $$h$$ above earth surface is the same as that at depth $$x (x \quad or\quad h < R_e),$$ then

At some planet, $$g = 1.96\ ms^{-2}$$. If it is safe to jump from a height of  $$2\ m$$ on earth, then the corresponding safe height on that planet is

If $${ W }_{ 1 }$$, $${ W }_{ 2 }$$ and $${ W }_{ 3 }$$ represent the work done in moving a particle from $$A$$ to $$B$$ along three different paths $$1$$, $$2$$ and $$3$$, respectively, (as shown in the figure) in the gravitational field of a point mass $$m$$, find the correct relation between $${ W }_{ 1 }$$, $${ W }_{ 2 }$$ and $${ W }_{ 3 }$$

If $$g$$ is same at a height $$h$$ and at a depth $$d$$, then

A missile is launched with a velocity less than the escape velocity from earth. The sum of its kinetic energy and potential energy is

A satellite S is moving in an elliptical orbit around the earth. The mass of the satellite is very small as compared to the mass of the earth.

If the escape velocity from the surface of a spherical planet is given by $$2 \displaystyle \sqrt{\frac{GM}{K}}$$, where $$M$$ is the mass of the planet and $$K$$ is a constant, then the radius of the planet is