(i) Since, space station and astronauts have equal acceleration, they are under free fall condition.
(ii) Both the astronauts and the space station are in the state of weightlessness.
(iii) They are not actually floating but falling freely around the earth due to the huge orbital velocity.

(i) Catching a cricket ball the fielder lowers his hands backwards. Because, he stops his hands soon after catching the ball, the ball comes to rest very quickly.
(ii) It means that the momentum of the ball is brought to rest very quickly.
(iii) So the average force acting on the body will be large.
(iv) Due to this large average force, the hands will get hurt.
(v) To avoid getting hurt, the player brings the ball to rest slowly.

(i) A spanner has a long handle to produce a larger moment of force by a small force applied normally at the end of its handle.
(ii) Moment of force = \(\overrightarrow{\mathbf{F}} \times \overrightarrow{\mathrm{d}}\)

Given: The ratio of masses of two planets \(M_{1}: M_{2} \) is 2: 3 The ratio of their radii \(R_{1}: R_{2}\) is 4: 7
\(g_{1}: g_{2}= ? \)
\(\mathrm{g}=\frac{\mathrm{G \times M}}{\mathrm{R}^{2}} ; \quad \mathrm{g}_{1}=\frac{\mathrm{G\times M}_{1}}{\mathrm{R}_{1}^{2}} ; \quad \mathrm{g}_{2}=\frac{\mathrm{G \times M}_{2}}{\mathrm{R}_{2}^{2}} \)
\(\frac{g_{1}}{g_{2}}=\frac{\frac{G \times M_{1}}{R_{1}^{2}}}{\frac{G \times M_{2}}{R_{2}^{2}}} ; \quad \frac{g_{1}}{g_{2}}=\frac{M_{1}}{R_{1}^{2}} \times \frac{R_{2}^{2}}{M_{2}}=\frac{2 \times 7 \times 7}{4 \times 4 \times 3}=\frac{49}{24}\)
∴ \(g_{1}: g_{2}\) = 49: 24

\(\text { Given } \quad \mathrm{F}_{1} =140 \mathrm{~N}  \)
\(\mathrm{~d}_{1} =40 \mathrm{~cm}=40 \times 10^{-2} \mathrm{~m}  \)
\(\mathrm{~F}_{2} =40 \mathrm{~N}  \)
\(\mathrm{~d}_{2} =?\)
The moment of force on the nut,
\(=F_{1} \times d_{1}=140 \times 40 \times 10^{-2}  \)
\(=56 \ \mathrm{Nm}\)
The same moment of force is required to unscrew the nut,
\(\mathrm{F}_{2} \times \mathrm{~d}_{2}  =40 \times d_2\)
In both cases, moment of forces applied are equal,
F₁ x d₁ = F₂ x d₂
56 = F₂d₂
\(56=40 \times \mathrm{d}_{2}  \)
\(\mathrm{~d}_{2}=\frac{56}{40}=1.4 \mathrm{~m}  \)
\(\mathrm{~d}_{2}=1.4 \mathrm{~m}\)
The spanner with the longer handle requires very less force to unscrew the same nut.

Given \(\mathrm{m}=1 \mathrm{~kg}, \quad \mathrm{v}=10 \mathrm{~m} \mathrm{~s}^{-1}\)
When a ball bounces back with the same speed, the momentum changes from mv to -mv. So, the change in momentum is -2 mv.
Δp = mv - mu
= -mv - mv
\(=-2 \mathrm{mv}=-2 \times 1 \times 10 \)      \([Here \ mu = mv \\ mv = -mv]\)
\(\therefore \Delta P=-20 \mathrm{~kg} \mathrm{~m} \mathrm{~s}^{-1}\)

Definition:
The inherent property of a body to resist any change in its state of rest or the state of uniform motion, unless it is influenced upon by an external unbalanced force, is known as inertia.
Types of Inertia:
(i) Inertia of rest
(ii) Inertia of motion
(iii) Inertia of direction
(i) Inertia of rest: The resistance of a body to change its state of rest is called inertia of rest.
Example: When you vigorously shake the branches of a tree, some of the leaves and fruits are detached and they fall down (Inertia of rest).
(ii) Inertia of motion: The resistance of a body to change its state of motion is called inertia of motion.
Example: An athlete runs some distance before jumping. Because, this will help him jump longer and higher (Inertia of motion).
(iii) Inertia of direction: The resistance of a body to change its direction of motion is called inertia of direction.
Example: When we make a sharp turn while driving a car we tend to lean sideways 'inertia of direction'.