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Physics Class 11 – Set A (Morning) – MCQs with Answer Key (September 2025)

Multiple Choice Questions (1 Mark Each)

Q1. Which of these have maximum number of significant figures?
(a) 10020
(b) 2.2500
(c) 0.001010
(d) 300000000

Q2. The result of 4.237 ÷ 2.51 keeping in view the number of significant figures will be:
(a) 1.688
(b) 1.7
(c) 1.69
(d) 1.68805

Q3. The dimensions of a and b in the relation F = at + bx are:
(a) [T] and [L]
(b) [MLT⁻³] and [MT⁻²]
(c) [MT⁻³] and [MLT⁻³]
(d) [ML²T⁻³] and [MLT⁻¹]

Q4. If velocity of a particle is constant in direction but not in magnitude, the path is:
(a) Circular
(b) Straight line
(c) Parabola
(d) Data incomplete

Q5. Which of the following changes when a particle moves with uniform velocity?
(a) Speed
(b) Velocity
(c) Acceleration
(d) Position

Q6. If three vectors add up to zero resultant, they:
(a) Must be in same straight line
(b) Must form a triangle when connected
(c) Must be perpendicular
(d) Can’t be in same plane

Q7. In projectile motion of a particle:
(a) Both velocity and acceleration change
(b) Velocity same, only acceleration changes
(c) Neither changes
(d) Only velocity changes

Q8. Magnitude of displacement of a particle:
(a) Always equal to distance
(b) Always less than distance
(c) Always greater than distance
(d) May be equal to distance

Q9. If net external force on a body is zero:
(a) Acceleration = 0
(b) Acceleration may be non-zero
(c) Velocity may change
(d) Velocity must change

Q10. Newton’s 2nd law states rate of change of momentum is proportional to:
(a) Angular momentum
(b) Torque
(c) Force
(d) Impulse

Q11. Wrong statement about Newton’s 3rd law:
(a) Action = –Reaction
(b) They act at same instant
(c) They cancel to give zero resultant
(d) They never cancel each other

Q12. If net external force on a system is zero:
(a) Linear momentum conserved
(b) Kinetic energy conserved
(c) All bodies come to rest
(d) System rotates in circle

Q13. A body of mass m at rest on a table experiences:
(a) Friction horizontally
(b) Friction vertically
(c) No friction
(d) Friction equal to weight

Q14. Two vectors are parallel and perpendicular if:
(a) Both dot and cross = 0
(b) Dot = 0 and Cross = 0
(c) Dot ≠ 0, Cross = 0
(d) Cross ≠ 0, Dot = 0

Q15. Work done by gravity depends on:
(a) Path taken
(b) Time taken
(c) Initial and final positions
(d) Agent moving body

Q16. A rigid body is one:
(a) Hard to chew
(b) Breaks other objects
(c) Distance between particles doesn’t change
(d) Doesn’t move on force

Q17. A bomb in parabolic path explodes in mid-air. Its centre of mass:
(a) Disappears
(b) Breaks into pieces
(c) Keeps moving in same parabola
(d) Reverses path

Q18. If angular velocity = ω, I = moment of inertia, v = linear velocity, then K.E. rotation is:
(a) ½ mv²
(b) ½ mω²
(c) ½ Iv²
(d) ½ Iω²

Q19. A body is in rotational equilibrium if:
(a) Net force = 0
(b) Net torque = 0
(c) Centre of mass moves uniformly
(d) Rotates with constant angular acceleration

Q20. A girl on a rotating table pulls arms inward:
(a) Angular velocity decreases
(b) Table stops
(c) Girl falls
(d) Angular velocity increases

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Yes 👍 I’ll carefully recheck each MCQ with concepts so your blog has 100% accurate Answer Key.

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Physics Class 11 – MCQs (Rechecked with Final Answer Key)

Q1. Which has maximum significant figures?
→ (b) 2.2500 (5 significant figures)

Q2. 4.237 ÷ 2.51 = 1.688… Significant figures = 3 (least in divisor).
→ (b) 1.7

Q3. F = at + bx → [MLT⁻²] = a[T] + b[L]
a = [MLT⁻³], b = [MT⁻²]
→ (b)

Q4. Direction constant, magnitude changes → circular motion.
→ (a)

Q5. In uniform velocity, position changes.
→ (d)

Q6. For 3 vectors sum = 0 → must form a closed triangle.
→ (b)

Q7. Projectile motion: velocity changes, acceleration constant.
→ (a)

Q8. Displacement ≤ distance, may be equal.
→ (d)

Q9. Net external force = 0 → acceleration = 0.
→ (a)

Q10. Newton’s 2nd law: dp/dt ∝ force.
→ (c)

Q11. Wrong statement: Action–reaction do not cancel (since different bodies).
→ (c)

Q12. No external force → linear momentum conserved.
→ (a)

Q13. A body at rest on table, no friction (friction arises only if external force applied).
→ (c)

Q14. Parallel → cross = 0, dot ≠ 0. Perpendicular → dot = 0, cross ≠ 0.
→ (c)

Q15. Work by conservative force depends only on initial & final positions.
→ (c)

Q16. Rigid body: distance between particles does not change.
→ (c)

Q17. After explosion, centre of mass continues same parabolic path.
→ (c)

Q18. Rotational KE = ½ Iω².
→ (d)

Q19. Rotational equilibrium → net external torque = 0.
→ (b)

Q20. Girl pulls arms in → moment of inertia decreases → ω increases (conservation of angular momentum).
→ (d)

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✅ Final Answer Key

1 → b
2 → b
3 → b
4 → a
5 → d
6 → b
7 → a
8 → d
9 → a
10 → c
11 → c
12 → a
13 → c
14 → c
15 → c
16 → c
17 → c
18 → d
19 → b
20 → d

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Physics Class 11 — 2-Mark Questions 

Q2. What is the meaning of the statement that SI is a rational system of units? Give an example.
Answer (final):
SI is a coherent and rational system: its derived units are obtained from the base units by algebraic combination without additional numerical factors, and the system is set up so common physical laws are expressed simply.
Example: Force $F=ma$ → SI derived unit of force is $kg\cdot m/s^2$ = Newton (N).

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Q3. Van der Waals equation $(P + a/V^2)(V - b) = RT$. Find dimensions of $a$ and $b$.
Answer (final):
Pressure $P$ has dimension $[M L^{-1} T^{-2}]$. Volume $V$ has $[L^3]$.

• $a/V^2$ has same dimension as pressure, so $[a] = [P][V^2] = [M L^{-1} T^{-2}]\cdot[L^6]=[M L^5 T^{-2}].$

• $b$ has dimension of volume: $[b] = [L^3].$

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Q4. Write any two differences between speed and velocity.
Answer (final):

1. Nature: Speed is a scalar (magnitude only); velocity is a vector (magnitude + direction).

2. Sign & direction: Speed ≥ 0 always; velocity can be positive, negative or zero depending on direction.

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Q5. Greatest and least resultant of two forces are 10 N and 6 N. If each force is increased by 3 N, find resultant when they act at 90°.
Answer (final, with steps):
Let forces be $F_1$ and $F_2$.
$F_1+F_2 = 10$ and $|F_1-F_2|=6$. Solve → $F_1=8$ N, $F_2=2$ N.
After increase: $F_1'=11$ N, $F_2'=5$ N. At $90^\circ$, resultant $R=\sqrt{11^2+5^2}=\sqrt{146}\approx 12.08$ N.

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Q6. Two bodies of mass $m_1$ and $m_2$ have equal linear momenta. Find ratio of velocities and kinetic energies.
Answer (final):
Given $m_1 v_1 = m_2 v_2$.

• Velocity ratio: $\dfrac{v_1}{v_2}=\dfrac{m_2}{m_1}.$

• Using $KE = \dfrac{p^2}{2m}$, ratio of kinetic energies: $\dfrac{KE_1}{KE_2}=\dfrac{m_2}{m_1}.$

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Q7. What is spring constant of a spring? Give its SI unit.
Answer (final):
Spring constant $k$ = restoring force per unit extension: $k = F/x$.
SI unit: N·m⁻¹ (N/m).

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Q8. Describe moment of inertia of a body. What is its physical significance?
Answer (final):
Moment of inertia $I=\sum m_i r_i^2$ (or $I=\int r^2 dm$), where $r_i$ is perpendicular distance of mass element from axis.
Significance: It measures rotational inertia — resistance of a body to change its rotational motion (analogous to mass in linear motion).

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Q9. By dimensional method obtain an expression for centripetal force $F$ for a particle of mass $m$ moving with speed $v$ in a circle of radius $r$.

Answer:
Assume $F \propto m^a v^b r^c$. Dimensions:
$[F]=[M L T^{-2}], [m]=[M], [v]=[L T^{-1}], [r]=[L]$.
So $[M L T^{-2}] = [M]^a [L T^{-1}]^b [L]^c = M^a L^{b+c} T^{-b}.$
Equate exponents:
For $M:$ $1 = a$ → $a=1$.
For $T:$ $-2 = -b$ → $b=2$.
For $L:$ $1 = b + c = 2 + c$ → $c = -1$.
Thus $F = K m v^2 r^{-1}$. For centripetal force constant $K=1$:
$\boxed{F=\dfrac{mv^2}{r}}$.

(Alternate answer by students: $F=m\omega^2 r$ using $v=\omega r$.)

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Q10. Define angular velocity of a particle moving in a circle. Also find relation between linear and angular velocity. Give vector relation and direction of linear velocity.

Answer:
Definition: Angular velocity $\omega$ is rate of change of angular displacement: $\omega = \dfrac{d\theta}{dt}$ (rad/s).
Relation (scalar): Linear speed $v = \omega r$.
Vector relation: $\mathbf{v} = \boldsymbol{\omega} \times \mathbf{r}$.
Direction of $\mathbf{v}$: Tangent to the circle at the particle, perpendicular to the radius, given by right-hand rule from $\boldsymbol{\omega}$.

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Q11. (i) When do distance and displacement have same magnitude?

(ii) Can a body have constant speed but varying velocity? Explain with example.
(iii) Can a body have constant velocity but varying speed? Explain.
Answer:
(i) Distance = magnitude of displacement when motion is along a straight line in one direction (no change of direction) — e.g., uniform straight motion.
(ii) Yes. Speed (magnitude of velocity) can be constant while velocity (vector) changes if direction changes. Example: uniform circular motion — speed constant, direction (hence velocity) changes.
(iii) No. If velocity (vector) is constant then both magnitude and direction are fixed; so speed cannot vary. Constant velocity implies constant speed.

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Q12. A vehicle moving on a horizontal road with speed $v$. If coefficient of friction between tyres and road is $\mu$, show shortest stopping distance is $\dfrac{v^2}{2\mu g}$.

Answer (derivation):
Maximum retarding friction force $f_{max} = \mu mg$. This gives maximum deceleration $a = \dfrac{f_{max}}{m} = \mu g$. Using $v^2 = u^2 + 2as$ with final $v_f=0$, initial $u=v$, and $a = -\mu g$:
$0 = v^2 - 2\mu g\, s \Rightarrow s = \dfrac{v^2}{2\mu g}.$
Hence $\boxed{s = \dfrac{v^2}{2\mu g}}$.

(If asked, numerical substitution can be done.)

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Q13. Apparent weight of a person of mass $m$ in a lift:

(a) moving upward with uniform acceleration $a$
(b) moving downward with uniform acceleration $a$ ($a<g$)
(c) falling freely under gravity.
Answer:
Let normal reaction = $N$ (apparent weight). Equation: $N - mg = ma_{\text{frame}}$.
(a) Upward acceleration $+a$: $N = m(g + a)$.
(b) Downward acceleration $-a$: $N = m(g - a)$.
(c) Free fall $a = g$: $N = m(g - g) = 0$.

So:
$\boxed{N = m(g+a),\; m(g-a),\; 0}$ respectively.

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Q14. State and prove work–energy theorem.

Answer (statement): Net work done by all forces on a particle equals change in its kinetic energy: $W_{\text{net}} = \Delta K = \tfrac{1}{2}m(v_f^2 - v_i^2)$.

Proof (brief): For motion along a line, net force $F = ma$. Work done by net force over small displacement $dx$: $dW = F\,dx = m a\, dx$. But $a = dv/dt$ and $dx = v\,dt$, so
$dW = m \dfrac{dv}{dt} v dt = m v\, dv$. Integrate from initial v_i to v_f:
$W = \int_{v_i}^{v_f} m v\, dv = \tfrac{1}{2}m(v_f^2 - v_i^2) = \Delta K.$
Hence proved.

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Q15. Calculate the power of a crane in watts, which lifts a mass of 100 kg to a height of 10 m in 20 seconds.

Answer:
Work done $= m g h = 100 \times 9.8 \times 10 = 9800$ J.
Power $P = \dfrac{Work}{time} = \dfrac{9800}{20} = 490$ W.
$\boxed{P = 490\ \text{W}}$.

(Alternate OR question on elastic collision: if you want, I can also provide that worked solution — tell me and I’ll add it.)

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Q16. Comprehension Type Question – Answer

The kinetic energy of rotation of a rigid body about a fixed axis is given by the formula $K.E. = \tfrac{1}{2} I \omega^2$, where $I$ is the moment of inertia of the body and $\omega$ is its angular velocity. The moment of inertia of a body about an axis is defined as the sum of the products of the masses of its particles and the squares of their perpendicular distances from that axis, that is $I = \sum m_i r_i^2$. Its SI unit is $kg \, m^2$ and its dimensional formula is $[M L^2]$. The moment of inertia of a body depends on several factors such as the position and orientation of the axis of rotation, the shape and size of the body, and the distribution of mass about the axis. It is considered as a measure of the rotational inertia of the body because it plays the same role in rotational motion as mass plays in linear motion. Just as mass resists changes in linear motion, moment of inertia resists changes in rotational motion, hence it can be regarded as the quantitative measure of rotational inertia of a body.

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(i) Write the formula of kinetic energy of rotation.

Answer:

$$K.E. = \tfrac{1}{2} I \omega^2$$

where $I$ = moment of inertia, $\omega$ = angular velocity.

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(ii) Define moment of inertia of a body.

Answer:
Moment of inertia of a body about a given axis is the sum of products of each particle’s mass and square of its perpendicular distance from the axis:

$$I = \sum m_i r_i^2$$

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(iii) Find the units and dimensions of moment of inertia.

Answer:

• Unit: $kg \, m^2$

• Dimensions: $[M L^2]$

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(iv) Write any two factors on which moment of inertia of a body depends.

Answer:

1. Position and orientation of axis of rotation.

2. Distribution of mass about the axis.

(Also depends on shape and size of body.)

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(v) Why can moment of inertia be regarded as measure of rotational inertia of the body?

Answer:
Because $I$ plays the same role in rotational motion as mass plays in linear motion:

• Larger $I$ means greater resistance to change in rotational state.
  Thus, it quantifies rotational inertia.

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Section E – 5 Marks Questions

Q17. What is projectile motion? Prove that the trajectory of a projectile projected at an angle $\theta$ with the horizontal is a parabola. Hence derive its time of flight and horizontal range.

OR
From the velocity–time graph of a particle having initial velocity $u$ moving with uniform acceleration in a straight line, derive the relations:
(i) $v = u + at$
(ii) $s = ut + \tfrac{1}{2} at^2$.
Also make graphs of $v$ vs $t$, and $s$ vs $t$.

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Q18. What is meant by banking of roads? Explain the need for it. Obtain an expression for the maximum speed with which a vehicle can safely negotiate a curved road banked at angle $\theta$. The coefficient of friction between road and wheels is $\mu$.

OR
Define angle of friction and angle of repose with the help of free-body diagrams. Find their values in terms of coefficient of friction $\mu$.

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