wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If mass and radius of the Earth are 6.0×1024 kg and 6.4×106 m respectively, calculate the force exerted by the Earth on a body of mass 1 kg. Also, calculate acceleration produced in the body of mass 1 kg and acceleration produced in the Earth.


A

9.8 and 1 respectively

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

9.8 and respectively

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C

and 9.8 respectively

No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

9.8 for both

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B

9.8 and respectively


From Newton's law of gravitation, we know that the force of attaraction between two bodies is given by:
F = Gm1m2r2
Here, m1 = mass of Earth = 6.0×1024 kg and m2 = mass of the body = 1 kg
r = distance between the two bodies = radius of the Earth = 6.4×106 m
G = 6.67×1011 Nm2kg2
F = 6.67×1011×6.0×1024×1(6.4×106)2 = 9.8 N
This shows that the Earth exerts a force of 9.8 N on a body of mass 1 kg. The body will exert an equal attractive force of 9.8 N on the Earth.
Acceleration produced in the body of mass 1 kg:
Force = mass × acceleration
Therefore, Acceleration, a = Fm = F1 = 9.8 ms2
Thus, the acceleration produced in a body of mass 1 kg due to attraction of the Earth is 9.8 ms2, which is quite large. Thus, when a body is released, it falls towards the Earth with an acceleration of 9.8 ms2, which can be easily observed.
Acceleration produced in the Earth:
Similarly, acceleration of the Earth is given by ForceMass of Earth = 9.86.0×1024 = 1.63×1024 ms2
This shows that the acceleration produced in the Earth by a body of mass 1 kg is 1.63×1024 ms2 which is very small and cannot be observed.


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Second Law of Motion
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon