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**Multiple Choice Questions**

**Q.1. Two objects of different masses falling freely near the surface of moon would (a) have same velocities at any instant (b) have different accelerations (c) experience forces of same magnitude (d) undergo a change in their inertia Ans:** (a)

(a) gravitational potential

(b) acceleration due to gravity

(c) gravitational field

(d) universal gravitational constant

Here point masses are separated by unit distance

Hence m1, m2 and r = 1

Hence F = G which is a universal constant hence answer is universal gravitational constant

(a) zero

(b) infinite

(c) R times the weight at the surface of the earth

(d) 1/R2 times the weight at surface of the earth

Ans:

(a) 2 N

(b) 8 N

(c) 10 N

(d) 12 N

Ans:

= 10N - 8N

= 2N

(a) maximum when length and breadth form the base

(b) maximum when breadth and width form the base

(c) maximum when width and length form the base

(d) the same in all the above three cases

Ans:

(a) F1 is very much greater than F2

(b) F2 is very much greater than F1

(c) F1 is only a little greater than F2

(d) F1 and F2 are equal

Ans:

**Short Answer Questions**

**Q.16. What is the source of centripetal force that a planet requires to revolve around the Sun? On what factors does that force depend? Ans:** Gravitational force is the source of centripetal force required to revolve around the sun. This force depends on the distance between the planet and sun along with their masses. If this force becomes zero as a result of the absence of centripetal force, the planet would shift to moving tangentially outwards to the circular route.

Ans:

Ans:

Ans:

This proves acceleration due to gravity on the moon is 1/6

g = GM /R

M = gR

Density of earth D= mass/volume

= Gr

= gR

= 3g/4µGR

Ans:

**Long Answer Questions**

**Q.23. 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?****Ans: **Let R and M be the radius and mass of the earth

Then

Weight of the object = M/R^{2}

Original weight W_{0} = mg = mg M/R^{2}

Hypothetically 4m and R becomes R/2

Then, weight = mG 4M /(R/2) ^{2}

= (16m g) M/R^{2}

= 10xW_{0}

Weight will be 16 times.**Q.24. 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.****Ans:**

The hypothesis is incorrect. Force of attraction between two masses separated by distance r is given by Newton law of gravitation where F= Gm1m2/R^{2} Where G is gravitational force and it is an universal constant.

Gravitational force is directly proportional to the product of the masses of two bodies and inversely proportional to the square of the distance between them.

Bodies thrown from same height fall with same speed irrespective of their mass. This is due to acceleration due to gravity.

g = GM/R^{2 }Where M is mass R is radius of the earth

This equation shows that acceleration due to gravity depends on the mass of the earth and radius of the earth. Hence tow brick tied will not fall faster than the single one.**Q.25. 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.****Ans: **

As the acceleration remains the same, the ratio between two objects remains the same. In this case, acceleration does not depend upon mass and size.**26. (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 weighing 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 m s^{–2})**

p = Density of water, V = Volume of water displaced by the body

Volume and density of an object decides its Buoyancy. Cube will experience a greater buoyancy in a saturated solution. If the cube is reduced to 4 cm on each side, the volume of cube becomes less as the buoyancy will be reduced as buoyant force is directly proportional to volume.

(ii) The magnitude of the buoyant force given by F = Vpg

where V = Volume of body immersed in water or volume of water displaced, p = Density of liquid.

[∴ Given, mass of a ball = 4 kg, density = 4000 kgm

Hence Volume of solid = mass/density

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