Answer:
the mass of the body is 0.02 kg.
Explanation:
Given;
relative density of the oil,
= 0.875
mass of the object in oil,
= 0.013 kg
mass of the object in water,
= 0.012 kg
let the mass of the object in air = 
weight of the oil, 
weight of the water, 
The relative density of the oil is given as;

Therefore, the mass of the body is 0.02 kg.
Answer:
![r_{cm}=[12.73,12.73]cm](https://tex.z-dn.net/?f=r_%7Bcm%7D%3D%5B12.73%2C12.73%5Dcm)
Explanation:
The general equation to calculate the center of mass is:

Any differential of mass can be calculated as:
Where "a" is the radius of the circle and λ is the linear density of the wire.
The linear density is given by:

So, the differential of mass is:


Now we proceed to calculate X and Y coordinates of the center of mass separately:


Solving both integrals, we get:


Therefore, the position of the center of mass is:
![r_{cm}=[12.73,12.73]cm](https://tex.z-dn.net/?f=r_%7Bcm%7D%3D%5B12.73%2C12.73%5Dcm)
Explanation:
The given data is as follows.
Velocity of bullet,
= 814.8 m/s
Observer distance from marksman, d = 24.7 m
Let us assume that time necessary for report of rifle to reach the observer is t and will be calculated as follows.
t =
(velocity in air = 343 m/s)
= 0.072 sec
Now, before the observer hears the report the distance traveled by the bullet is as follows.

= 
= 58.66
= 59 (approx)
Thus, we can conclude that each bullet will travel a distance of 59 m.
To find the ratio of planetary speeds Va/Vb we need the orbital velocity formula:
V=√({G*M}/R), where G is the gravitational constant, M is the mass of the distant star and R is the distance of the planet from the star it is orbiting.
So Va/Vb=[√( {G*M}/Ra) ] / [√( {G*M}/Rb) ], in our case Ra = 7.8*Rb
Va/Vb=[ √( {G*M}/{7.8*Rb} ) ] / [√( {G*M}/Rb )], we put everything under one square root by the rule: (√a) / (√b) = √(a/b)
Va/Vb=√ [ { (G*M)/(7.8*Rb) } / { (G*M)/(Rb) } ], when we cancel out G, M and Rb we get:
Va/Vb=√(1/7.8)/(1/1)=√(1/7.8)=0.358 so the ratio of Va/Vb = 0.358.