1. The force of gravitation between two objects is inversely proportional to the square of the distance between them therefore the gravity will become four times if distance between them is reduced to half.
2. In free fall of objects the acceleration in velocity due to gravity is independent of mass of those objects hence a heavy object does not fall faster than a light object.
4. The earth and the moon are attracted to each other by same gravitational force because for both of them formula to calculate force of attraction is the same
d is also same for both.
5. Earth does not move towards moon because mass of moon is very small as compared to that of earth.
6. (i) the force between two objects will be doubled.
(ii) the force between two objects will become 1/4th and 1/9th of the present force.
(iii) the force between two objects will become four times the present force.
7. The universal law of gravitation is important due to the following :
(i) this law explains well the force that binds us to earth.
(ii) this law describes the motion of planets around the sun.
(iii) this law justifies the tide formation on earth due to moon and sun.
(iv) this law gives reason for movement of moon around earth.
8. The acceleration of free fall is g = 9.8 m/s2 (on earth)
10. Since W = m x g and given in the question that value of g is greater at the poles than at the equator, hence weight of same amount of gold will be lesser at equator than it was on the poles. Therefore, the friend will not agree with the weight of gold bought.
11. A greater surface area offers greater resistance and buoyancy same is true in the case of a sheet of paper that has larger surface area as compared to paper crumpled into a ball. So sheet of paper falls slower.
12. value of gravity on earth = 9.8 m/s2
value of gravity on moon = 1/6th of earth = 9.8/6 = 1.63 m/s2
weight of object on moon = m × 1.63 = 10 × 1.63 = 16.3 N
weight of object on earth = m × 9.8 = 10 × 9.8 = 98 N
13. (i) v = u + gt
0 = 49 + (―9.8) × t
9.8t = 49
t = 49/9.8 = 5 s
h = ut + ½ gt2 = 49 × 5 + ½ × 9.8 × 25 = 245 – 122.5 = 122.5
(ii) Total time taken to return = 5 + 5 = 10s
14. h = ut + ½ gt2
19.6 = 0 × t + ½ × 9.8 × t2
4.9 t2 = 19.6
t2 = 19.6/4.9 = 4
t = 2
since v= u + at = 0 + 9.8 × 2 = 19.6m/s
15. Initial velocity of stone (u) = 40 m/s
at maximum height stone will be at rest so v= 0
v = u + gt
0 = 40 + (-10) × t
10t = 40
t = 40/10 = 4 s
distance covered /maximum height
h = ut + 1/2gt2
= 40 × 4 + ½ × (-10) × 4 × 4 = 160 – 80 = 80 m
net displacement of stone = 0(thrown upwards then falls back to same place) total distance covered by the stone = 80 + 80 = 160 m
17. Suppose both the stones will meet after t seconds.
h = ut + ½ gt2
= 0 x t + ½ × 10 × t2
h’ = ut + ½ gt2
= 25 × t + ½ × (-10) × t2
= 25t – 5t2
h + h’ = 100 m
5t2 + 25t – 5t2 = 100
25t = 100
t = 4 s
h = 5t2 = 5 × 4 × 4 = 80 m
Therefore the two stones will meet after 4 seconds when the falling stone would have covered a height of 80 m.
18. (a) time taken by ball to reach maximum height(t) = 6/2 = 3 s
v = u + gt
0 = u + (-9.8) × 3
u = 29.4 m/s (the velocity with which it was thrown up)
(b) the maximum height it reaches: therefore h = ut + ½ gt2
= 29.4 × 3 + ½ × (-9.8) × 32
= 88.2 – 44.1
= 44.1 m
(c) its position after 4 s will be:
Since in first 3 s it will reach the maximum height and in next 1 s it will start a free fall so, u = 0, t = 1
h = ut + ½ gt2
= 0 × t + ½ × 9.8 × 1 = 4.9 m
therefore after 4s the position of ball = 44.1 – 4.9 = 39.2 m
19. In the upward direction only.
20. Since of plastic has density very less as compared to water i.e. weight of plastic is less than the buoyant force experienced by it therefore a block of plastic released under water come up to the surface of water/floats.
21. Density of that substance (d) = mass/volume = 50/20 = 2.5 g /cm3
since the density of substance (2.5) is greater than the density of water (1) therefore it will sink.
22. Density of the packet = mass/volume = 500/350 = 1.428 g/cm3
Since the density of packet is more than density of water so it will sink. And packet will displace water equal to its volume:
volume of water displaced by packet = 350 cm3 (volume of packet)
mass of water displaced = volume of water displaced × density of water = 350 × 1 = 350 g
23. According to Newton’s universal law of gravitation:
Every mass in this universe attracts every other mass with a force which is directly proportional to the product of two masses and inversely proportional to the square of the distance between them.
24. The formula to find the magnitude of the gravitational force between the earth and an object on the surface of the earth is given below:
F = magnitude of gravitational force
G = Universal gravitation constant
M = mass of earth
m = mass of object
d = distance of object from the centre of earth
25. It is the object falling towards earth under the influence of attraction force of earth or gravity.
26. During free fall any object that has mass experiences forces towards centre of earth and hence an acceleration works as well. “acceleration experienced by an object in its free fall is called acceleration due to gravity.” It is denoted by g.
27. Mass of object
(i) Mass is defined as quantity of matter contained in an object.
(ii) It is denoted by ‘m’.
(iii) F = m × a
(iv) It remains constant at any place of the universe.
Weight of object
(i) Weight is the force with which an object is attracted towards the earth’s centre.
(ii) It is denoted by ‘W’.
(iii) W = m × g
(iv) It is different at different places.
28. Since we know
W = m × g
Mass of object remains the same whether on earth or moon but the value of acceleration on moon is 1/6th of the value of acceleration on earth. Because of this weight of an object on moon is 1/6th its weight on the earth.
29. It is difficult to hold a school bag having a strap made of a thin and strong string because a bag of that kind will make its weight fall over a small area of the shoulder and produce a greater pressure that makes holding the bag difficult and painful.
30. It is the upward force experienced by an object when it is immersed into a fluid.
31. As an object comes in contact with the surface of a fluid it experiences two types of forces: gravitational force or gravity that pulls the object in downward direction and the second force is the force of buoyancy that pushes the object in upward direction. It is these two forces that are responsible for an object to float or sink
i.e. if gravity >buoyancy then object sinks
if gravity <buoyancy then object floats
32. Mass will be slightly more than 42 kg.
33. The bag of cotton is heavier since volume of cotton bag is greater than iron bar, so the upthrust is larger in case of cotton hence real mass of cotton bag is more and it is heavier.