Density of the 500 g sealed packet= Mass of the Packet / Volume of the Packet
= 500 / 350
= 1.428 g cm⁻³
The density of the substance is more than the density of water (1 g cm⁻³). Hence, it will sink in water.
The mass of water displaced by the packet is equal to the volume of the packet, i.e., 350 g.

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) have same velocities at any instant
Explanation: When an object is under free fall, its acceleration depends only on the acceleration due to gravity and mass has no role to play. Due to this; irrespective of their masses, the object under free fall will have same velocity at any instant.

2. The value of acceleration due to gravity
(a) is same on equator and poles
(b) is least on poles
(c) is least on equator
(d) increases from pole to equator
Ans. (c) is least on equator
Explanation: The distance between surface of earth and its centre is more on equator than on the poles. Moreover, g varies inversely as square of radius. Due to this, acceleration due to gravity is least on equator.

3. The gravitational force between two objects is F. If masses of both objects are halved without changing distance between them, then the gravitational force would become
(a) F/4
(b) F/2
(c) F
(d) 2 F
Ans. (a) F/4
Explanation: Gravitational force between two object varies directly as their masses and inversely as the square of distance between them. So, when the masses of both objects are halved without changing the distance, the gravitational force between them would become one-fourth of the original value.

4. A boy is whirling a stone tied with a string in an horizontal circular path. If the string breaks, the stone
(a) will continue to move in the circular path
(b) will move along a straight line towards the centre of the circular path
(c) will move along a straight line tangential to the circular path
(d) will move along a straight line perpendicular to the circular path away from the boy
Ans. (c) will move along a straight line tangential to the circular path

Explanation: When an object is in circular motion, it tends to be in rectilinear motion at any instance of time. This is due to the centripetal force that the object remains moving on the circular path but when the string breaks, the stone will move along a straight line tangential to the circular path.

5. An object is put one by one in three liquids having different densities. The object floats with 1/9, 2/11, and 3/7 parts of their volumes of outside the liquid surface in liquids of densities d1, d2 and d3 respectively. Which of the following statement is correct?
(a) d1> d2> d3
(b) d1> d2< d3
(c) d1< d2> d3
(d) d1< d2< d3
Ans. (d) d1< d2< d3


Explanation: Let us find LCM of fractions of volumes outside the liquid surface in each other.

LCM of denominator is 693 and using this, the fractions can be written as follows:

This shows that these fractions are arranged in ascending order. Hence, densities of liquids are in ascending order.


6. In the relation F= G M m/d2, the quantity G
(a) depends on the value of g at the place of observation
(b) is used only when the earth is one of the two masses
(c) is greatest at the surface of the earth
(d) is universal constant of nature
Ans. (d) is universal constant of nature

7. Law of gravitation gives the gravitational force between
(a) the earth and a point mass only
(b) the earth and Sun only
(c) any two bodies having some mass
(d) two charged bodies only
Ans. (c) any two bodies having some mass

8. The value of quantity G in the law of gravitation
(a) depends on mass of earth only
(b) depends on radius of earth only
(c) depends on both mass and radius of earth
(d) is independent of mass and radius of the earth
Ans. (d) is independent of mass and radius of the earth

Explanation: Since G is a universal constant, hence its value does not depend on mass or radius of the earth.
9. Two particles are placed at some distance. If the mass of each of the two particles is doubled, keeping the distance between them unchanged, the value of gravitational force between them will be
(a) � times
(b) 4 times
(c) � times
(d) unchanged
Ans. (b) 4 times

Explanation: Gravitational force between two objects varies directly as their masses and inversely as the square of distance between them. So, when the masses of both objects are doubled without changing the distance, the gravitational force between them would become four times of the original value.

10. The atmosphere is held to the earth by
(a) gravity
(b) wind
(c) clouds
(d) earth�s magnetic field
Ans. (a) gravity

11. The force of attraction between two unit point masses separated by a unit distance is called
(a) gravitational potential
(b) acceleration due to gravity
(c) gravitational field
(d) universal gravitational constant
Ans. (d) universal gravitational constant

12. The weight of an object at the centre of the earth of radius R is
(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) zero
Explanation: The acceleration due to gravity is zero at the centre of the earth. We know that weight is a product of mass and g. Hence, when g = 0, weight would be zero.

13. An object weighs 10 N in air. When immersed fully in water, it weighs only 8 N. The weight of the liquid displaced by the object will be
(a) 2 N
(b) 8 N
(c) 10 N

(d) 12 N
Ans. (a) 2 N
Explanation: The weight of liquid displaced by object = weight in air � weight in liquid
=10 N � 8 N = 2 N. Moreover, according to Archimedes� theory; when an object is immersed in water, there is apparent reduction in its weight and the reduction is equal to the weight of liquid displaced by the object.

14. A girl stands on a box having 60 cm length, 40 cm breadth and 20 cm width in three ways. In which of the following cases, pressure exerted by the brick will be
(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. (b) maximum when breadth and width form the base

Explanation: Pressure is inversely proportional to surface area. When surface area is minimum then pressure will be maximum. Hence, option (b) is the correct answer.

15. An apple falls from a tree because of gravitational attraction between the earth and apple. If F1 is the magnitude of force exerted by the earth on the apple and F2 is the magnitude of force exerted by apple on earth, then

(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. (d) F1 and F2 are equal
Explanation: This is in accordance to Newton�s Third Law of Motion which states that for every action there is an equal and opposite reaction.

Gravitational force. This force depends on the product of the masses of the planet and sun and the distance between them.

Both stones will take the same time to reach the ground because the two stones fall from the same height.

The moon will begin to move in a straight line in the direction in which it was moving at that instant because the circular motion of moon is due to centripetal force provided by the gravitational force of earth.

The value of ‘g’ at the equator of the earth is less than that at poles. Therefore, the packet falls slowly at equator in comparison to the poles. Thus, the packet will remain in air for longer time interval, when it is dropped at the equator.

Since the weight of any person on moon is about 1/6 times that on the earth, hence acceleration due to gravity at moon is 1/6 of that on earth. This means that by applying the same force a person can lift six times heavier object on the moon than what he could lift on the earth. So, the maximum mass which can be lifted by the same force applied by
the person on the moon is 6 × 15 kg = 90 kg.