Problem on Gravitation for Class 9

By Jitender Singh on Jan 03, 2023

Useful constants: $G=6.67\times10^{-11}$ N m² kg^-2, $M_\text{earth}=5.98\times10^{24}$ kg, $R_\text{earth}=6.37\times10^{6}$ m, $M_\text{moon}=7.36\times10^{22}$ kg, $R_\text{moon}=1.74\times10^{6}$ m, $M_\text{sun}=2\times10^{30}$ kg.

1. The mass of the earth is $6\times10^{24}$ kg and that of the moon is $7.4\times10^{22}$ kg. If the distance between the earth and the moon is $3.84\times10^5$ km, calculate the force exerted by the earth on the moon. ($G=6.67\times10^{-11}$ N m² kg^-2).
2. What is the magnitude of the gravitational force between the earth and a 1 kg object on its surface? (Take $G=6.67\times10^{-11}$ N m² kg^-2, $M_\text{earth}=5.98\times10^{24}$ kg, $R_\text{earth}=6.37\times10^{6}$ m)
3. Calculate the force of gravitation between the earth and the Sun, given that the mass of the earth $=6\times10^{24}$ kg and of the Sun $=2\times10^{30}$ kg. The average distance between the two is $1.5\times10^{11}$ m.
4. A car falls off a ledge and drops to the ground in 0.5 s. Let $g=10$ m/s². (i) What is its speed on striking the ground? (ii) What is its average speed during the 0.5 s? (iii) How high is the ledge from the ground?
5. An object is thrown vertically upwards and rises to a height of 10 m. Calculate (i) the velocity with which the object was thrown upwards and (ii) the time taken by the object to reach the highest point.
6. A ball is thrown vertically upwards with a velocity of 49 m/s. Calculate (i) the maximum height to which it rises (ii) the total time it takes to return to the surface of the earth
7. A stone is released from the top of a tower of height 19.6 m. Calculate its final velocity just before touching the ground.
8. A stone is thrown vertically upward with an initial velocity of 40 m/s. Taking $g=10$ m/s², find the maximum height reached by the stone. What is the net displacement and the total distance covered by the stone?
9. A stone is allowed to fall from the top of a tower 100 m high and at the same time another stone is projected vertically upwards from the ground with a velocity 25 m/s. Calculate when and where the two stones will meet.
10. A ball is thrown up vertically returns to the thrower after 6 s. Find (i) the velocity with which it was thrown up (ii) the maximum height it reaches, and (iii) its position after 4 s.
11. Mass of an object is 10 kg. What is its weight on the earth?
12. An object weighs 10 N when measured on the surface of the earth. What would be its weight when measured on the surface of the moon?
13. Gravitational force on the moon is only 1/6 as strong as gravitational force on the earth. What is the weight in newtons of a 10 kg object on the moon and on the earth?
14. A block of wood is kept on a tabletop. The mass of wooden block is 5 kg and its dimensions are 40 cm $\times$ 20 cm $\times$ 10 cm. Find the pressure exerted by the wooden block on the table top if it is made to lie on the table top with its sides of dimensions (i) 20 cm $\times$ 10 cm and (ii) 40 cm $\times$ 20 cm.
15. Relative density of silver is 10.8. The density of water is $10^3$ kg/m³. What is the density of silver in SI units?
16. The volume of 50 g of a substance is 20 cm³. If the density of water is 1 g/cm³, will the substance float or sink?
17. The volume of a 500 g sealed packet is 350 cm³. Will the packet float or sink in water if the density of water is 1 g/cm³? What will be the mass of the water displaced by this packet?

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