Gravitation

A mass of 50 kg is placed at the centre of a uniform spherical shell of mass 100 kg and radius 50 m. If the gravitational potential at a point, 25 m from the centre is V kg/m. The value of V is :

Water falls from a 40 m high dam at the rate of 9 $\times$ 10⁴ kg per hour. Fifty percentage of gravitational potential energy can be converted into electrical energy. Using this hydroelectric energy number of 100 W lamps, that can be lit, is : (Take g = 10 ms^$-$2)

An object of mass $1 \mathrm{~kg}$ is taken to a height from the surface of earth which is equal to three times the radius of earth. The gain in potential energy of the object will be [If, $\mathrm{g}=10 \mathrm{~ms}^{-2}$ and radius of earth $=6400 \mathrm{~km}$ ]

An object is allowed to fall from a height $R$ above the earth, where $R$ is the radius of earth. Its velocity when it strikes the earth's surface, ignoring air resistance, will be

If the gravitational field in the space is given as $\left(-\frac{K}{r^{2}}\right)$. Taking the reference point to be at $\mathrm{r}=2 \mathrm{~cm}$ with gravitational potential $\mathrm{V}=10 \mathrm{~J} / \mathrm{kg}$. Find the gravitational potential at $\mathrm{r}=3 \mathrm{~cm}$ in SI unit (Given, that $\mathrm{K}=6 \mathrm{~Jcm} / \mathrm{kg}$)

A body of mass is taken from earth surface to the height h equal to twice the radius of earth (R$_e$), the increase in potential energy will be : (g = acceleration due to gravity on the surface of Earth)

A body is released from a height equal to the radius $(\mathrm{R})$ of the earth. The velocity of the body when it strikes the surface of the earth will be (Given $g=$ acceleration due to gravity on the earth.)

If $\mathrm{V}$ is the gravitational potential due to sphere of uniform density on it's surface, then it's value at the center of sphere will be:-

The gravitational potential at a point above the surface of earth is $-5.12 \times 10^7 \mathrm{~J} / \mathrm{kg}$ and the acceleration due to gravity at that point is $6.4 \mathrm{~m} / \mathrm{s}^2$. Assume that the mean radius of earth to be $6400 \mathrm{~km}$. The height of this point above the earth's surface is :

If $\mathrm{G}$ be the gravitational constant and $\mathrm{u}$ be the energy density then which of the following quantity have the dimensions as that of the $\sqrt{\mathrm{uG}}$ :