Final momentum on each object Δp = FΔt = 100\(\times\)5 = 500 kg ms^-1
Final speed on the object of mass 5 kg = 500/5 =100 m s^-1
Final speed on the object of mass 20 kg = 500/20 =25 m s^-1
Note that momentum on each object is the same after 5 seconds but speed is not the same after 5 seconds. The heavier mass acquires lesser speed than the one with lower mass.

The centripetal acceleration ac=\(\frac { { v }^{ 2 } }{ r } \)
V.- velocity of Earth around the orbit
r - radius of orbit or distance of Earth to Sun
Velocity of Earth is written in terms of angular velocity (ω) as
v-ωr
By substituting in the centripetal acceleration formula, ac=\({ a }_{ c }=\frac { { \omega }^{ 2 }{ r }^{ 2 } }{ r } =\omega ^{ 2 }\)=ω²r
But ω=\(\frac { 2\pi }{ T } \) where T is time for the Earth to orbit around the sun, which is one year.
T = 365 days = 365\(\times\)24\(\times\)60\(\times\)60s
T = 31\(\times\)10⁷ s
(ω)= 2.02\(\times\)10^-7 rad per see
a_c = (2.02\(\times\)10^-7)² \(\times\)(150\(\times\)10⁸)
a_c= 6.12\(\times\)10^-4 ms^-2

To find the force, we need to find the acceleration experienced by the particle.
Th e acceleration is given by a=\(\frac { { d }^{ 2 }y }{ { dt }^{ 2 } } \) or a=\(\frac { dv }{ dt } \)
Here v = velocity of the particle in y direction
v = \(\frac { dy }{ dt } \) = u - gt
The momentum of the particle = mv = m(u - gt)
a = \(\frac { dv }{ dt } \) = -g
The force acting on the object is given by F = ma = -mg
The negative sign implies that the force is acting on the negative y direction. This is exactly the force that acts on the object in projectile motion.

Given, \(\vec { F } =(6\hat { i } -8\hat { j } +10\hat { k } )\)
m = \(\frac { |\vec { F } | }{ a } =\frac { \sqrt { { 6 }^{ 2 }+{ 8 }^{ 2 }+{ 10 }^{ 2 } } }{ 1 } =10\sqrt { 2 } \) kg

m = 150g = 0.15 kg
u = 15 ms-1, v = 0, t=0.05s
Impulse = m(v-u)
=0.15 (0-15) = -2.25 NS
Average force = \(\frac { Impulse }{ Time } =\frac { -2.25 }{ 0.05 } \) = -45N
The negative sign indicates the retarding nature of the force.

Rolling friction < Sliding friction

μ = tanθ
\(\frac { 1 }{ \sqrt { 3 } } \) = tanθ
 θ = 30⁰

The acceleration is the second derivative of position vector of the body \(\left( \bar { a } =\frac { { d }^{ 2 }\vec { r } }{ dt^{ 2 } } \right) \) the force on the body is \(\vec { F } =m\frac { { d }^{ 2 }\vec { r } }{ { dt }^{ 2 } } \).
If \(\frac { { d }^{ 2 }r }{ d{ t }^{ 2 } } \neq 0\) , F≠0.

If an object is thrown vertically upward, the direction of motion is upward, but gravitational force is downward.

force and direction of motion are in opposite direction

(i) If multiple forces \(\overset { \rightarrow }{ { F } } _{ 1 },\overset { \rightarrow }{ { F } } _{ 2 },\overset { \rightarrow }{ { F } } _{ 3 }...\overset { \rightarrow }{ { F } } _{ n }\) act on the same body, then the total force \(\left( \overset { \rightarrow }{ { F }_{ net } } \right) \) is equivalent to the vectorial sum of the individual forces
(ii) Their net force provides the acceleration. \(\overset { \rightarrow }{ { F } } _{ net }=\overset { \rightarrow }{ { F } } _{ 1 },\overset { \rightarrow }{ { F } } _{ 2 },\overset { \rightarrow }{ { F } } _{ 3 }...\overset { \rightarrow }{ { F } } _{ n }\)
(iii) Newton's second law for this case is \(\overset { \rightarrow }{ { F } } _{ net }=m\overset { \rightarrow }{ a } \)
In this case the direction of acceleration is in the direction of net force.

(i) Two spring balances are attached.
(ii) One end is fixed with rigid support and the other free end pulled by the force.
(iii) Pull one end with same force and note the readings on both the balances.
(iv) Repeat it. We can notice same reading in both balances.

As per Newton's Third Law of Motion every action has an equal and opposite reaction. As this law is valid on the physical plane in the physical science, it equally holds well but not completely in the metaphysics and in the spiritual science. In the physical plane, the action and reaction are instantaneous; one follows the other without significant time lapse, where as in the metaphysical science there is always a time lag between actions and their reactions. The complete Karmic theory, the theory of actions and reactions, is closely linked and follow the principle of Newton's Third law of equal actions and reactions.
The only difference and additional parameter in the Karmic theory. of actions/ reactions is "inertia or time lapse" of reactions, which has made it more complex and has created confusion in the mind of a common man. Sometimes reaction cannot be easily linked with the action because the reaction may be entirely different from the action executed. Furthermore, actions done on physical plane, mental plane and on intellectual plane bring different reactions in the metaphysical science. It must be experienced and understood by metaphysical science that behind every action there is a divine force. This force acts on us by His grace similar to the Newton's Third Law of physical science as a result of our past actions and it is governed by the inertial forces with time lag, which varies very widely and is beyond the perception of a common human being. Newton's third law is applicable to only human's actions which involves physical force. Third law is not applicable to human's psychological actions or thoughts.

Force acting vertically to sling shot
Tension T in each string;
Now applying Lami's theorem, we get
\(\frac{2 T}{\sin \theta} =F  \)
\(\frac{2 T}{\sin (2 \times 30)} =50 N  \)
\(\frac{2 T}{\sin (60)} =50 N  \)
\(\frac{2 T}{\sqrt{3}} =50 N  \)
\(\frac{T}{2 T} =\frac{2}{\sqrt{3}} \times 50 N  \)
\(T=\frac{50 N}{\sqrt{3}}=28.268 N\)

T = mg
T = 50g x 9.8m/s²
Tension (T) = 0.49 N