[3 Mark Question Answer]

Question 13 Marks

$(i)\ (a)$ Study the diagram alongside and calculate the moment of couple.

$(b)$ Two forces $F_1= F_2$ are applied on a wheel of radius $1.5\ m,$ such that moment of couple is $30\ Nm$. Calculate the magnitude of each of the force.
$(ii)\ A$ force of $50\ N$ produces a moment of force of $10\ Nm$ in a rigid body. Calculate the perpendicular distance between the point of application of force and the turning point.
$(iii)\ (a)$ State the laws of moments.
$(b)$ The diagram shows a wheel of diameter $4\ m,$ and pivoted at $O$. Calculate the moment of force about point $(1)\ O, (2)\ Q,$ when a force$ F = 4N$ acts at point $P$ or $Q$.

Answer

$(i)\ (a)$
Moment of couple $=$ Force $\times$ arm of couple
$ =5\ N \times 1.2\ m$ in $\text{ACWD}$
$ =6\ Nm$ in $\text{ACWD}$
$(b)$ Radius of the wheel $=1.5\ m$; Moment of couple $=30\ Nm$
Arm of couple $=$ diameter of the wheel $=1.5\ m \times 2=3.0\ m$
Magnitude of each of the force; $F = F _1= F _2=\frac{\text { Moment of couple }}{\perp \text { distance }}=\frac{30 Nm }{3.0}=10 N$.
$(ii)$ Given$, F =50\ N$; Moment of force $=10\ Nm$
$\therefore \perp$ distance $=\frac{\text { moment of force }}{\text { force }}=\frac{10 Nm}{50\ N}=0.2\ m$
$(iii)\ (a)$ When number of forces are acting on a body, such that body is in equilibrium, then sum total moments of forces in clockwise direction is equal to sum total of anticlockwise moment of forces.
$(b)$ Diameter of wheel $=4\ m$ ;
$\therefore$ Radius of wheel $-2\ m$
$1.$ Moment of force about point $O = F\ \times \perp$ distance $=4\ N \times 2\ m=8\ Nm$ in $\text{ACWD}$
$2.$ Moment of force about point $Q = F\ \times \perp$ distance between $O$ and $Q$
$=4 N \times 2\ m=8\ Nm$ in $\text{ACWD}.$

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Question 23 Marks

(i) Define equilibrium and briefly discuss types of equilibrium.
(ii) Compare uniform circular motion and uniform linear motion.
(iii) Explain the motion of moon around the earth.

Answer

(i) When number of forces (two or more) act on a rigid body, such that it does not changes its state of rest or uniform motion, the rigid body is said to be in equilibrium
There can be two kinds of equilibrium i.e.,
(a) Static equilibrium (b) dynamic equilibrium
(a) Static equilibrium: When a body remains in its state of rest when two or more forces are acting on it then the body is said to be in static equilibrium.
(b) Dynamic equilibrium: When a body remains in its uniform state of motion (translational or rational) when two ( or more forces are acting on it, the body is said to be in dynamic equilibrium.
(ii) Comparison of uniform circular motion and uniform linear motion

S.No.	Uniform circular motion	Uniform linear motion
1	The speed of a body is constant	Speed of the body is constant.
2	Velocity of a body is variable.	Velocity of the body is constant
3	Acceleration of the body is non-zero.	Acceleration of the body is zero.
4	Force acts towards the centre of circular path.	No external force is required.

(iii) The moon moves around the earth in a near circular path. The gravitational force of the earth acts on the moon and provides the necessary centripetal force.

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Question 33 Marks

Study the diagram alongside carefully and calculate the resultant moment of force about:
(a) point P
(b) point Q
(c) about point R which is exactly in the middle of P and Q.

Answer

(a) Moment of force due to $F _1$ about $P = F _1 \times \perp$ distance
$=20 N \times 0=0$
Moment of force due to $F _2$ about $P = F _2 \times \perp$ distance $=20 N \times \frac{20}{100} m=4 Nm$ in C.W.D.
$\therefore$ Resultant moment of force about $P =0+4 Nm =4 Nm$ in C.W.D.
(b) Moment of force due to $F _1$ about $Q = F _1 \times \perp$ distance $=20 N \times \frac{20}{100} m=4 Nm$ in CWD Moment of force due to $F _2$ about $Q = F _2 \times \perp$ distance $=20 N \times 0=0$
$\therefore$ Resultant moment of force about $Q =4 Nm +0=4 Nm$ in C.W.D.
(c) Moment of force due to $F _1$ about $R = F _1 \times \perp$ distance $=20 N \times \frac{10}{100} m=2 Nm$ in CWD Moment of force due to $F _2$ about $R = F _2 \times \perp$ distance $=20 N \times \frac{10}{100} m=2 Nm$ in CWD
$\therefore$ Resultant moment of force about $R =2 Nm +2 Nm =4 Nm$ in C.W.D.

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Question 43 Marks

(a) What do you understand by the term equilibrium of a body?
(b) State the condition when a body is in (i) dynamic equilibrium (ii) static equilibrium. Support your answer with one example each.
(c) A body is acted upon by number of forces acting in different directions. State two conditions for a body to be in equilibrium.

Answer

(a) If a body continues in its state of rest or of uniform motion even after the application of external forces, then the body is said to be in equilibrium.
(b) A body is in
(i) Dynamic equilibrium: If the body remains in its state of uniform motion, after the application of several forces.
Example - Raindrops fall with a uniform speed because the weight of the raindrop is counterbalanced by the buoyant force of the air and friction of air.
(ii) Static equilibrium: If the body remains in its state of rest, after the application of two or more forces.
Example - A block of wood in static equilibrium under number of forces. The applied force is counterbalanced
(c) (i) The resultant of all the translational forces acting on the rigid body should be zero.
(ii) The resultant of moment of rotational forces acting on the rigid body should be zero, i.e., all clockwise moments should be equal to all anticlockwise moments.

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Physics [3 Mark Question Answer]

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