Gravitation NCERT Solution, study material, CBSE Notes

NCERT Solution: Gravitation

The earth is acted upon by gravitation of Sun, even though it does not fall into the Sun. Why?

The gravitational of the sun provides the necessary centripetal force to keep the earth in its orbit. This counters the centrifugal force which arises due to circular motion of the earth. Thus, earth remains on its orbit without either falling into the sun or going away tangentially to its orbit.

How does the weight of an object vary with respect to mass and radius of the earth. In a hypothetical case, if the diameter of the earth becomes half of its present value and its mass becomes four times of its present value, then how would the weight of any object on the surface of the earth be affected?

Weight of a body α M /R²

The weight will become 16 times.

How does the force of attraction between the two bodies depend upon their masses and distance between them? A student thought that two bricks tied together would fall faster than a single one under the action of gravity. Do you agree with his hypothesis or not? Comment.

F α m1 m2

F α 1/d²
This hypothesis is not correct. The two bricks, like a single body, fall with the same speed to reach the ground at the same time in case of free-fall. This is because acceleration due to gravity is independent of the mass of the falling body

Two objects of masses m1 and m2 having the same size are dropped simultaneously from heights h1 and h2 respectively. Find out the ratio of time they would take in reaching the ground. Will this ratio remain the same if (i) one of the objects is hollow and the other one is solid and (ii) both of them are hollow, size remaining the same in each case? Give reason.

Ratio will not change in either case because acceleration remains the same. In case of free-fall acceleration does not depend upon mass and size

A cube of side 5 cm is immersed in water and then in saturated salt solution. In which case, will it experience a greater buoyant force

(a) A cube of side 5 cm is immersed in water and then in saturated salt solution. In which case, will it experience a greater buoyant force. If each side of the cube is reduced to 4 cm and then immersed in water, what will be the effect on the buoyant force experienced by the cube as compared to the first case for water. Give reason for each case.
(b) A ball weight 4 kg of density 4000 kg m^-3 is completely immersed in water of density 10³ kg m^-3. Find the force of buoyancy on it. (Given g = 10 ms^-2.)

Ans. (a) (i) The cube will experience a greater buoyant force in the saturated salt solution because the density of the salt solution is greater than that of water.
(ii) The smaller cube will experience lesser buoyant force as its volume is lesser than the initial cube.
(b) Buoyant force = weight of the liquid displaced
= density of water � volume of water displaced �g