Answer:
1.38*10^18 kg
Explanation:
According to the Newton's law of universal gravitation:

where:
G= Gravitational constant (6.674×10−11 N · (m/kg)2)
ma= mass of the astronaut
mp= mass of the planet

so:

let the length of the beam be "L"
from the diagram
AD = length of beam = L
AC = CD = AD/2 = L/2
BC = AC - AB = (L/2) - 1.10
BD = AD - AB = L - 1.10
m = mass of beam = 20 kg
m₁ = mass of child on left end = 30 kg
m₂ = mass of child on right end = 40 kg
using equilibrium of torque about B
(m₁ g) (AB) = (mg) (BC) + (m₂ g) (BD)
30 (1.10) = (20) ((L/2) - 1.10) + (40) (L - 1.10)
L = 1.98 m
Answer:
102 kg.m/s
Explanation:
m = Mass of hammer = 12 kg
v = Final velocity = 8.5 m/s
u = Initial velocity = 0
t = Time taken = 8 ms
Force acting over a given amount of time or change in momentum is known as impulse.
Impulse

Impulse given to the nail is 102 kg.m/s
Answer:
The positive displacement from the midpoint of its motion at the speed equal one half of its maximum speed is 3.56 cm.
Explanation:
Maximum speed is :
v (max) = Aω
Speed v at any displacement y is given by
=
(
-
) ........................................................ i
And,
v =
v (max)
or, 2 × v = Aω .................................................... ii
Eliminating ω from equations i and ii,
=
(
-
)
or,
= (
)
=(
) 
or, y = 3.56 cm.