Maharashtra Board Solutions for Chapter: Gravitation, Exercise 10: Exercise

Let the period of revolution of a planet at a distance $R$ from a star be $T$. Prove that if it was at a distance of $2R$ from the star, its period of revolution will be $\sqrt{8}T$.

An object takes $5 \mathrm{s}$ to reach the ground from a height of $5 \mathrm{m}$ on a planet. What is the value of $g$ on the planet?

The radius of planet A is half the radius of planet B. If the mass of A is $M_A$, what must be the mass of B so that the value of $g$ on B is half that of its value on A?

The mass and weight of an object on earth are $5 \mathrm{kg}$ and $49 \mathrm{N}$ respectively. What will be their values on the moon? Assume that the acceleration due to gravity on the moon is ${\frac{1}{6}}^{\mathrm{th}}$ of that on the earth.

An object thrown vertically upwards reaches a height of $500 \mathrm{m}$. What was its initial velocity? How long will the object take to come back to the earth? Assume $g=10 \mathrm{m} {\mathrm{s}}^{-2}$.

A ball falls off a table and reaches the ground in $1 \mathrm{s}$. Assuming $g=10 \mathrm{m} {\mathrm{s}}^{-2}$, calculate its speed on reaching the ground and the height of the table.

The masses of the earth and moon are $6\times {10}^{24} \mathrm{kg}$ and $7.4\times {10}^{22} \mathrm{kg}$, respectively. The distance between them is $3.84\times {10}^5 \mathrm{km}$. Calculate the gravitational force of attraction between the two. Use $G=6.7\times {10}^{-11} \mathrm{N} {\mathrm{m}}^2 {\mathrm{kg}}^{-2}$.

The mass of the earth is $6\times {10}^{24} \mathrm{kg}$. The distance between the earth and the Sun is $1.5\times {10}^{11} \mathrm{m}$. If the gravitational force between the two is $3.5\times {10}^{22} \mathrm{N}$, what is the mass of the Sun? Use $G=6.7\times {10}^{-11} \mathrm{N} {\mathrm{m}}^2 {\mathrm{kg}}^{-2}$.