Formula: The moment of a force M = F × d
Given: F = 40 N and d = 90 cm = 0.9 m.
Hence, moment of the force = 40 × 0.9 = 36 N m.

Linear momentum = mass × velocity
Velocity = linear momentum / mass. V = 2.5 / 5 = 0.5 m s^-1

(i) Let M be the mass of the Earth and m be the mass of the object.
(ii) The entire mass of the earth is assumed to be concentrated at its centre. The radius of the earth is R (= 6378 km = 6400 km approximately).
(iii) By Newton's law of gravitation, the force acting on the object is given by
F = G M m / R²  ............. (A)
(iv) According to Newton's second law, the force acting on the object is given by the product of its mass and acceleration. Here acceleration of the is under action of gravity hence a =g.
F=ma =mg
F = weight = mg
Comparing equations (A) and (B), we get
g= GM/ R²
Acceleration due to gravity
g=\(\frac { GM }{ { R }^{ 2 } } \).

(i) When birds fly they push the air downwards by their wings (Action).
(ii) The air pushes the bird upwards (Reaction).
(iii) When a person swims he pushes the water using hands backwards (Action), the water pushes the swimmer in forward direction (Reaction).
(iv) Rockets expel gas at high velocity (Action). The downward moving gas pushes the rocket in upward direction (Reaction).
(v) When we fire a bullet, the gun recoils back, Bullet is moving forward (action). The gun equalise this forward action by moving backward (reaction).

(i) Gears: A gear is a circular wheel with teeth around its rim. It helps to change the speed of rotation of a wheel by changing the torque and helps to transmit power.
(ii) Seesaw: When the heavier person comes closer to the pivot point (fulcrum) the distance of the line of action of the force decreases. It causes less amount of torque to act on it. This enables the lighter person to lift the heavier person.
(iii) Steering Wheel: A small steering wheel enables you to manoeuore a car easily by transferring a torque to the wheels with less effort.

(i) The natural state of all earthly objects is either the state of rest or the state of uniform motion.
(ii) An object in motion will continue to be in the same state of motion as long as no external force is applied.
(iii) When force is applied on objects, they resist any change in their state. This property of objects is called "inertia".
(iv) When dropped from a height in vacuum, objects of different size, shape and mass fall at the same rate arid reach the ground at the same time.

Data: Height from the centre of the Earth,
R' = R + h
The acceleration due to gravity at that height, g' = g/4'
Formula: g = GM /R², gʹ = GM /Rʹ2
\(\frac { g }{ g' } =\left( \frac { R' }{ R } \right) ^{ 2 }={ \left( \frac { R+h }{ R } \right) }^{ 2 }={ \left( 1+\frac { h }{ R } \right) }^{ 2 }\)
\(4=\left( 1+\frac { h }{ R } \right) ^{ 2 },\)
\(2=1+\frac { h }{ R } \quad or\quad h=R.\quad R'=2R\)
From the centre of the Earth, the object is placed at twice the radius of the earth.

Force, F = 50 N
Distance, d = 5 cm
To find: Momentum of force= F x d
Momentum of force, 50 x 5 x 10^-2
= 250 x 10^-2
= 2.5 Nm

Given:
Mass of the ball, m = 150 g
m = 150 x 10^-3 kg
Initial speed of the ball, u = 12 ms^-1
Final speed of the ball, v = -20 rns^-1
[-ve sign indicates backward direction]
To find: Impulse, J =?
Impulse = Change in linear momentum
= mv-mu
= Final momentum - Initial momentum
= m(v-u)
= 150 x 10^-3 [-20 - 12]
= 150  x 10^-3 x -32
J = -4.8 kg ms^-1