1. 0.16 N
The weight of a man on the surface of asteroid is equal to the gravitational force exerted on the man:

where
G is the gravitational constant
is the mass of the asteroid
m = 100 kg is the mass of the man
r = 2.0 km = 2000 m is the distance of the man from the centre of the asteroid
Substituting, we find

2. 1.7 m/s
In order to stay in orbit just above the surface of the asteroid (so, at a distance r=2000 m from its centre), the gravitational force must be equal to the centripetal force

where v is the minimum speed required to stay in orbit.
Re-arranging the equation and solving for v, we find:

Answer:
B'=1.935 T
Explanation:
Given that
magnetic field ,B= 0.645 T
We know that magnetic filed in the solenoid is given as

I=Current
n=Number of turn per unit length
μ0 =magnetic permeability
Now when the current increased by 3 factors
I'=3 I
Then the magnetic filed


B'=3 B
That is why
B' = 3 x 0.645 T
B'=1.935 T
Therefore the new magnetic filed will be 1.935 T.
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Answer:
a) Diffusion coefficient, D = 1.5 in/hr
b) Mean jump frequency, f = 0.0833 Hz
Explanation:
a) The relationship between the diffusion coefficient, time and mean displacement and can be given by the expression:
..........(1)
Where <r> = mean displacement
D = Diffusion coefficient
t = time = 12 hrs
sum of the squares of the distance divided by 100 is 36 in2.
<r>²= 36 in²
Substituting these values into equation (1) above

b) Mean jumping distance, <r> = 0.1 inches
Applying equation (1) again
Where D = 1.5 in/hr


The mean jump frequency, f = 1/t
f = 1/12
f = 0.0833 Hz
Answer:
The velocity of the astronaut is, v = - 0.36 m/s
Explanation:
Given data,
The mass of the astronaut, M = 84 kg
The mass of the gas expelled by the thruster, m = 35 g
= 0.035 g
The velocity of the gas expelled, v = 875 m/s
According to the conservation of momentum,
MV + mv = 0
V = - mv / M
Substituting the values,
V = - 0.035 x 875 / 84
= - 0.36 m/s
The negative sign in the velocity indicates the astronaut moves opposite to the direction of velocity of gas.
Hence, the velocity of the astronaut is, v = - 0.36 m/s