If mass and radius of the Earth are 6.0 x 10“ kg and 6.4 x 106 m respectively. Calculate the force exerted by the Earth on a body of mass 1 kg, acceleration of the body of mass 1 kg and acceleration of the Earth in order. Use G= 6.67 x 10-11
Answers
Answer:
From Newton's law of gravitation, we know that the force of attraction between two bodies is given by
F
=
G
m
1
m
2
r
2
Here, m1 = mass of earth =
6.0
∗
10
24
kg;
m2 = mass of body = 1 kg
r = distance between the two bodies
= radius of earth =
6.4
∗
10
6
m
G =
6.67
∗
10
−
11
N
m
2
k
g
2
F
=
6.67
∗
10
−
11
∗
6.0
∗
10
24
∗
1
(
6.4
∗
10
6
)
2
= 9.8 N
This shows that earth exerts a force of 9.8 N on a body of mass of 1 kg. The body will exert an equal force of attraction of 9.8 N on earth.
(i) Acceleration produced in the body of mass 1kg
Force = mass × acceleration
Therefore, acceleration a =
F
m
=
F
1
= 9.8
m
s
2
Thus, the acceleration produced in a body of mass 1 kg due to attraction of earth is
9.8
m
s
2
, which is quite large. Thus, when a body is released, it falls towards the earth with an acceleration of 9.8
m
s
2
, which can be easily observed.
(ii) Acceleration produced in the earth
Similarly, acceleration of earth is given by
=
F
o
r
c
e
M
a
s
s
o
f
e
a
r
t
h
=
9.8
6.0
∗
10
24
1.63 ×
10
−
24
m
s
2
This shows that the acceleration produced in the earth by a body of mass 1 kg is
1.63 ×
10
−
24
m
s
2
which is very small and cannot be observed.
Explanation:
Answer:
Explanation:
From Newton's law of gravitation, we know that the force of attraction between two bodies is given by
F
=
G
m
1
m
2
r
2
Here, m1 = mass of earth =
6.0
∗
10
24
kg;
m2 = mass of body = 1 kg
r = distance between the two bodies
= radius of earth =
6.4
∗
10
6
m
G =
6.67
∗
10
−
11
N
m
2
k
g
2
F
=
6.67
∗
10
−
11
∗
6.0
∗
10
24
∗
1
(
6.4
∗
10
6
)
2
= 9.8 N
This shows that earth exerts a force of 9.8 N on a body of mass of 1 kg. The body will exert an equal force of attraction of 9.8 N on earth.
(i) Acceleration produced in the body of mass 1kg
Force = mass × acceleration
Therefore, acceleration a =
F
m
=
F
1
= 9.8
m
s
2
Thus, the acceleration produced in a body of mass 1 kg due to attraction of earth is
9.8
m
s
2
, which is quite large. Thus, when a body is released, it falls towards the earth with an acceleration of 9.8
m
s
2
, which can be easily observed.
(ii) Acceleration produced in the earth
Similarly, acceleration of earth is given by