# HBSE Class 11 Physics Question Paper 2024 Answer Key

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HBSE Class 11 Physics Question Paper 2024 Answer Key

Section – A (1 Mark)

1. A car accelerated from rest at 2 m/s2. How far will it travel in 5 second?
(a) 10 m
(b) 25 m
(c) 50 m
(d) 100 m
s = ut + ½at2 = 0×5 + ½(2)(5)2 = 25 m

2. A particle completes circular path of radius r displacement of particle will be :
(a) 2πr
(b) 2π
(c) πr
(d) zero

3. The angles of projection for which a projectile covers the same horizontal range, are 30° and ……………..
(a) 45°
(b) 60°
(c) 75°
(d) 90°
Sum of angle of projection = 30° + 60° = 90°

4. If external force on a body is zero, its acceleration is :
(a) F/m
(b) m/F
(c) F
(d) Zero
Force = mass × acceleration
a = F/m = 0/m = 0

5. A 5 kg block is pulled over a surface with a friction coefficient of 0.2 with a force of 10 N. Calculate the friction force :
(a) 1 N
(b) 5 N
(c) 10 N
(d) 20 N
Friction force = coefficient of friction × normal force
F = μ.N = μ.mg = 0.2 × 5 × 9.8 = 9.8N ≈ 10N (approx.)

6. What is the kinetic energy of a 2 kg object moving at a velocity of 3 m/s ?
(a) 6 J
(b) 9 J
(c) 18 J
(b) 27 J
K.E = ½mv2 = ½(2)(3)2 = 9 Joules

7. When a conservative force does positive work on a body, the potential energy of the body :
(a) increases
(b) decreases
(c) remains unaltered
(d) None

8. Value of acceleration due to gravity with increasing depth from earth surface :
(a) increases
(b) decreases
(c) remains unaltered
(d) None

9. According to Kepler’s law of period (T) :
(a) T ∝ R2
(b) T ∝ R3
(c) T ∝ R1/2
(d) T ∝ R3/2
Answer – (d) T ∝ R3/2  (or T2 ∝ R3)

10. Two 10 kg masses are separated by a distance of 1 metre. Calculate the gravitational force between them :
(a) 6.67 × 10–11 N
(b) 6.67 × 10–10 N
(c) 6.67 × 10–9 N
(d) 6.67 × 10–8 N
Answer – (c) 6.67 × 10–9 N
F = Gm1m2/r2 = 6.67×10–11 × 10 × 10/(1)2 = 6.67 × 10–9 N

11. If a wire is stretched to double of its length, then its Young’s Modulus of Elasticity will be :
(a) Half
(b) Same
(c) Two times
(d) Four times

12. Two soap bubbles have radii in the ratio 2 : 1. What is the ratio of excess-pressure inside them?
(a) 1 : 2
(b) 2 : 1
(c) 1 : 4
(d) 4 : 1
Answer – (a) 1 : 2
Excess pressure, P = 4T/R
P ∝ 1/R
P1 : P2 = R2 : R1 = 1 : 2

13. After terminal velocity is reached, the acceleration of a body falling through a viscous fluid is :
(a) zero
(b) equal to g
(c) less than g
(d) greater than g

14. An adiabatic process occurs at constant :
(a) Temperature
(b) Pressure
(c) Heat
(d) Temperature and Pressure

15. Assertion (A) : Air quickly leaking out of a balloon becomes cooler.
Reason (R) : The leaking air undergoes adiabatic expansion..
(a) Both (A) and (R) are true and (R) is the correct explanation of (A).
(b) Both (A) and (R) are true and (R) is not the correct explanation of (A).
(c) (A) is true but (R) is false.
(d) (A) is false and (R) is also false.
Answer – (a) Both (A) and (R) are true and (R) is the correct explanation of (A).

16. Assertion (A) : Work and heat are two equivalent form of energy.
Reason (R) : Work is the transfer of mechanical energy irrespective of temperature difference, whereas heat is the transfer of thermal energy because of temperature difference only.
(a) Both (A) and (R) are true and (R) is the correct explanation of (A).
(b) Both (A) and (R) are true and (R) is not the correct explanation of (A).
(c) (A) is true but (R) is false.
(d) (A) is false and (R) is also false.
Answer – (a) Both (A) and (R) are true and (R) is the correct explanation of (A).

17. Assertion (A) : All small oscillation are simple harmonic in nature.
Reason (R) : Oscillation of spring block system are always simple harmonic, whether amplitude is small or large.
(a) Both (A) and (R) are true and (R) is the correct explanation of (A).
(b) Both (A) and (R) are true and (R) is not the correct explanation of (A).
(c) (A) is true but (R) is false.
(d) (A) is false and (R) is also false.
Answer – (d) (A) is false and (R) is also false.

18. Assertion (A) : An oscillatory motion is necessarily periodic.
Reason (R) : A simple harmonic motion is necessarily oscillatory.
(a) Both (A) and (R) are true and (R) is the correct explanation of (A).
(b) Both (A) and (R) are true and (R) is not the correct explanation of (A).
(c) (A) is true but (R) is false.
(d) (A) is false and (R) is also false.
Answer – (b) Both (A) and (R) are true and (R) is not the correct explanation of (A).

Section – B (2 Marks)

19. The displacement x of a particle is given by x = a + bt + ct2, where t is time in second and displacement x is in metre. Find dimension of a and b.
Answer – By principle of homogeneity,
a = x = [L]
bt = x = [L]
b = x/t = [LT –1]

20. Suppose that the period (T) of oscillation of the simple pendulum depends on its length (L), mass of the bob (m) and acceleration due to gravity (g). Derive expression for its time period using method of dimensions.

21. Derive the work-energy theorem for a variable force.

OR

Write relation between kinetic energy and momentum and with the help of this relation, answer, if the momentum of a lighter and heavy body are same, then K. E. of which body will be greater?

22. What is Elastic Potential Energy? Write its mathematical formula for spring having spring constant K.
Answer – Elastic Potential Energy is the potential energy stored in an elastic material when it is stretched or compressed. The amount of energy stored is proportional to the amount stretched or compressed. This type of potential energy arises due to the deformation of the object.
P.E. = Magnitude of Force × Displacement
P.E. = ½Kx2

OR

What is coefficient of restitution? Write its value for elastic collision.
Answer – The ratio of final velocity to the initial velocity between two objects after their collision is known as the coefficient of restitution. For elastic collision, e = 1

23. What is Surface Tension? Write its unit.
Answer – It is the tendency of fluid surface to shrink into the minimum surface area possible.
The force per unit length perpendicular to a line drawn in the surface of the liquid is the surface tension. Its SI unit is Newtons Per Metre (N/m).

24. What are the two assumptions of the kinetic theory of gases?
Answer – (i) The separation between the molecules is much greater than the size of the molecules.
(ii) Molecules of gas undergo perfect elastic collisions.
(iii) All the collisions between molecules and even between molecules and walls are considered to be elastic.

25. A steel wire 0.50 m long has a mass of 4 × 10–3 kg. If the wire is under a tension of 80 N. What is the speed of Transverse Waves on the wire?
Answer – Mass per unit length of the wire is
μ = M/L = 4×10–3/0.50 = 8 × 10–3 kg/m
Tension, T = 80 N
The speed of transverse wave on the wire is
v = √T/μ = √80/(8×10–3) = √10000 = 100 m/s

Section – C (3 Marks)

26. An object is moving with a constant acceleration, Draw time-acceleration, time-velocity and time-displacement graphs for the object.

27. Particles of masses m1 = 2 g, m2 = 2 g, m3 = 1 g and m4 = 1 g are placed at the corners of a square of side L, as shown. Find the centre of mass of the system with respect to m1.
Answer – Centre of mass M(x, y)
x = (m1x1 + m2x2 + m3x3 + m4x4) / (m1 + m2 + m3 + m4)
= (m1×0 + m2×L + m3×L + m4×0) / (m1 + m2 + m3 + m4)
= (m2+m3)L / (m1+m2+m3+m4)
= (2+1)L / (2+2+1+1)
= 3/6 L = L/2
y = (m1y1 + m2y2 + m3y3 + m4y4) / (m1 + m2 + m3 + m4)
= (m1×0 + m2×0 + m3×L + m4×L) / (m1 + m2 + m3 + m4)
= (m3+m4)L / (m1 + m2 + m3 + m4)
= (1+1)L / (2+2+1+1)
= 2/6 L = L/3
Centre of mass M(x, y) is (L/2, L/3).

28. State law of conservation of angular momentum. Explain its with the help of any one example.
Answer – It states that “For a spinning system, there is no change in the angular momentum of the object until and unless an external torque is applied to it”. Therefore, it can be stated that the velocity of the rotation will remain constant as long as the net torque applied is equal to zero.
Example, The spinning of an ice skater: An ice skater is spinning on the tip of her skate with her arms extended. Her angular momentum is conserved because the net torque on her is negligibly small. Her rate of spin increases greatly when she pulls in her arms, decreasing her moment of inertia. The work she does to pull in her arms results in an increase in rotational kinetic energy.

29. State Kepler’s laws of planetary motion.
Answer – Kepler’s laws of planetary motion describe the motion of planets around the Sun. There are three laws :
• Kepler’s First Law (Law of Ellipses) – Every planet orbits the Sun in an elliptical path, with the Sun at one of the two foci of the ellipse.
• Kepler’s Second Law (Law of Equal Areas) – A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. This means that a planet travels faster when it is closer to the Sun (perihelion) and slower when it is farther from the Sun (aphelion).
• Kepler’s Third Law (Law of Harmonies) – The square of the orbital period of a planet (the time it takes to complete one orbit around the Sun) is directly proportional to the cube of the semi-major axis of its orbit. Mathematically, this can be expressed as: T2 ∝ a

OR

What is meant by escape velocity for a planet? Establish expression for escape velocity of a body from the surface of earth.
Answer – Escape velocity for a planet is the minimum speed an object needs to reach in order to break free from the planet’s gravitational pull and move into space without falling back.

Here g = 9.8 m/s2 and R = 6.4 × 106 m
v = √2gR = √2×9.8×6.4×106 = 11.2 km/s
so, the escape velocity from Earth is about 11.2 km/s.

30. Write three differences between isothermal process and adiabatic process.

 Isothermal Process Adiabatic Process 1. Transfer of heat occurs. 1. No transfer of heat occurs. 2. The pressure is more at a given volume. 2. The pressure is less at a given volume. 3. The temperature remains constant. 3. The temperature changes due to internal system variations. 4. The transformation is slow. 4. The transformation is fast.

Section – D (5 Marks)

31. A projectile is thrown at an angle θ from the horizontal with velocity u under the gravitational field of earth. Find expression for time of flight and maximum height.
Answer – Time of flight (T) = 2usinθ/g
Maximum height (H) = u2sin2θ/2g

OR

State law of triangle vector addition and prove expression of resultant.
Answer – Triangle law of vector addition states that if two vectors are represented in magnitude and direction by two sides of a triangle taken in the same order, then their resultant is represented by the third side of the triangle taken in the opposite order.

32. State and prove Bernoulli’s theorem.

OR

State and prove Newton’s law of cooling.
Answer – Newton’s law of cooling describes the rate at which an exposed body changes temperature through radiation, which is approximately proportional to the difference between the object’s temperature and its surroundings, provided the difference is small.

33. What is limiting friction? State the laws of limiting friction.
Answer – Limiting friction is described as the friction created when two static surfaces come into contact with each other.
Laws of limiting friction :
• The direction of limiting friction force is always opposite the direction of motion.
• It always acts tangential to the two surfaces.
• It is dependent on the material and the nature of the surfaces in contact.
• It is independent of the shape and area.

OR

A man of mass 70 kg stands on a weighing scale in a lift which is moving (g = 10 m/s2) :
(a) upwards with a uniform speed of 10 m/s.
(b) downward with a uniform acceleration of 5 m/s2.
What would be the reading on the scale in each case?
Answer – (a) R = mg = 70 × 10 = 700 N
Reading on scale = 700/g = 700/10 = 70 kg
(b) R = m(g – a) = 70(10 – 5) = 350 N
Reading on scale = 350/g = 350/10 = 35 kg

Section – E (Case Study : 4 Marks)

34. The molecule of a monoatomic gas consist of a single atom. Its translational motion can take place in any direction in space. Thus it can be resolved along three coordinate axis and can have three independent motions. Hence it has three degree of freedom, all translational. The molecule of a diatomic gas is made up of two atoms joined rigidly to one another through a bond. This can not only move bodily, but also rotate about any of the three coordinate axes. A diatomic molecule has five degree of freedom, three with respect to translation and two with respect to rotation.
Questions :
(i) A diatomic molecule has degree of freedom :
(a) 2
(b) 3
(c) 4
(d) 5

(ii) The molecule of a monoatomic gas is :
(a) He
(b) H2
(c) O2
(d) CO2

(iii) Define degree of freedom.
Answer – The number of independent coordinates required to specify the position of particle or system of particles is known as degree of freedom. It is an independent physical parameter in the formal description of the state of a physical system.

OR

State law of equipartition of energy.
Answer – The law of equipartition of energy states that “For a system which is in thermal equilibrium, its total energy is divided equally among the degree of freedom”.

35.(a) The motion of the particle should be in a straight line to and fro about a fixed point.
(b) The restoring force acting on the particle should always be proportional to the displacement of the particle from that point.
(c) The force should always be directed towards that point.
These are the conditions of S. H. M.
Questions :
(i) Force which is always directed towards the equilibrium position is :
(a) Centripetal force
(b) Centrifugal force
(c) Normal force
(d) Restoring force

(ii) The rotation of the earth about its own axis is :
(a) periodic motion
(b) non-periodic motion
(c) circular motion
(d) linear motion