Class 11 Physics Sample Paper: Complete Solutions and Explanations
Section A: Multiple Choice Questions (1 Mark Each)
Q1. Multiple Choice Questions
I) Light year is a unit of
(a) Time (b) velocity (c) Distance (d) pressure
Answer: (c) Distance
Explanation: A light-year is the distance that light travels in one year, used to measure astronomical distances.
II) Which of the following quantities have the same dimensions as that of work?
(a) Force (b) energy (c) Stress (d) acceleration
Answer: (b) energy
Explanation: Work and energy have the same dimensions, which are [ML²T⁻²].
III) Number of significant figures in 6.0023 is
(a) 1 (b) 3 (c) 4 (d) 5
Answer: (d) 5
Explanation: All non-zero digits and zeros between them are significant. Hence, 6.0023 has five significant figures.
IV) A boy starts from a point A, travels to a point B at a distance of 3 km from A and returns to A. If he takes two hours to do so, his speed is
(a) 3 km/h (b) zero (c) 2 km/h (d) 1.5 km/h
Answer: (a) 3 km/h
Explanation: Speed = Total Distance / Total Time = (3 km + 3 km) / 2 hours = 6 km / 2 hours = 3 km/h.
V) Two vectors are said to be equal when
(a) When the vectors are acting in the opposite direction
(b) Both the vectors are acting at an angle of 45 degrees to each other
(c) When the vectors are at right angles
(d) When the vectors are parallel to each other with the same magnitude
Answer: (d) When the vectors are parallel to each other with the same magnitude
Explanation: Two vectors are equal if they have the same magnitude and direction.
VI) Coefficient of kinetic friction is
(a) more than the coefficient of static friction
(b) less than the coefficient of static friction
(c) Equal to the coefficient of static friction
(d) none of the above
Answer: (b) less than the coefficient of static friction
Explanation: The coefficient of kinetic friction is generally less than that of static friction.
VII) Angular displacement is measured in
(a) Radian (b) m (c) radian/s (d) none of the above
Answer: (a) Radian
Explanation: Angular displacement is measured in radians.
VIII) Relation for centripetal acceleration (a) in terms of linear velocity v and radius r of circular path is given by
(a) a=ur (b) a=vr² (c) a=v²/r (d) none of the above
Answer: (c) a=v²/r
Explanation: Centripetal acceleration is given by the formula a = v²/r.
IX) The friction is maximum in the case of
(a) static friction
(b) rolling friction
(c) sliding friction
(d) limiting friction
Answer: (d) limiting friction
Explanation: Limiting friction is the maximum value of static friction just before the object starts moving.
X) What is the average power required to lift a mass of 100kg to a height of 50m in 50 seconds?
(a) 100 Watt (b) 50 Watt (c) 980 Watt (d) 5000 Watt
Answer: (c) 980 Watt
Explanation: Power = Work / Time = (mgh) / t = (100 kg * 9.8 m/s² * 50 m) / 50 s = 980 Watt.
XI) On which of the following factors does the moment of inertia of an object not depend upon?
(a) Axis of rotation (b) Angular velocity
(c) Distribution of mass (d) Mass of an object
Answer: (b) Angular velocity
Explanation: The moment of inertia depends on the mass distribution and the axis of rotation, not on the angular velocity.
XII) When the torque acting on the system is zero, which of the following is constant?
(a) Linear impulse (b) Linear momentum (c) Force (d) Angular momentum
Answer: (d) Angular momentum
Explanation: When the net torque is zero, angular momentum is conserved.
XIII) If the distance between two masses is doubled, the gravitational attraction between them
(a) Is doubled (b) Becomes four times
(c) Is reduced to half (d) Is reduced to a quarter
Answer: (d) Is reduced to a quarter
Explanation: Gravitational force is inversely proportional to the square of the distance. Hence, if the distance is doubled, the force becomes one-fourth.
XIV) g does not depend upon:
(a) The mass of the earth (b) The shape of the earth
(c) The revolution period of the earth (d) The radius of the earth
Answer: (c) The revolution period of the earth
Explanation: The acceleration due to gravity (g) depends on the mass and radius of the earth, not on its revolution period.
XV) The rain drops are spherical due to
(a) Viscosity (b) surface tension
(c) Elasticity (d) excess pressure
Answer: (b) surface tension
Explanation: Surface tension minimizes the surface area, causing raindrops to form a spherical shape.
XVI) Heat given to the unit mass of a body which raises its temperature by 1°C is
(a) Water equivalent (b) thermal capacity
(c) Temperature gradient (d) specific heat
Answer: (d) specific heat
Explanation: Specific heat is the amount of heat required to raise the temperature of a unit mass by 1°C.
XVII) The amount of heat required to change the state of a substance without a change in temperature is known as
(a) Latent heat (b) specific heat capacity (c) internal energy (d) thermal energy
Answer: (a) Latent heat
Explanation: Latent heat is the heat required for a phase change without a temperature change.
XVIII) The state of a gas in thermodynamics is described by macroscopic variables such as:
(a) Pressure (b) Volume (c) temperature (d) all of the above
Answer: (d) all of the above
Explanation: The state of a gas is described by pressure, volume, and temperature.
XIX) The equation PV= constant at constant temperature is known as:
(a) Charles’s Law (b) Avogadro’s Law (c) Boyle’s Law (d) None
Answer: (c) Boyle’s Law
Explanation: Boyle’s Law states that at constant temperature, the product of pressure and volume is constant.
XX) The value of y (Cp/Cv) for monatomic gas is
(a) 1.33 (b) 1.5 (c) 1.67 (d) 1.8
Answer: (c) 1.67
Explanation: For a monatomic gas, the ratio of specific heats (γ) is 1.67.
XXI) Real gases obey ideal gas laws more closely at:
(a) High pressure and low temperature (b) Low pressure and high temperature
(c) High pressure and high temperature (d) Low pressure and low temperature
Answer: (b) Low pressure and high temperature
Explanation: Real gases behave like ideal gases at low pressure and high temperature.
XXII) The frequency of a wave is 0.002 Hz. Its time period is
(a) 100 s (b) 500 s (c) 5000 s (d) 50 s
Answer: (b) 500 s
Explanation: Time period (T) = 1 / frequency (f) = 1 / 0.002 Hz = 500 s.
XXIII) A particle of mass m is hanging vertically by an ideal spring of force constant K. If the mass is made to oscillate vertically, its total energy is
(a) Maximum at extreme position (b) Maximum at mean position
(c) Minimum at mean position (d) Same at all positions
Answer: (d) Same at all positions
Explanation: In simple harmonic motion, the total energy remains constant.
Section B: True/False Questions
I) The horizontal range of a projectile is maximum when fired at 60º with the horizontal.
Answer: False
Explanation: The horizontal range is maximum when fired at 45º.
II) Torque is a vector quantity.
Answer: True
Explanation: Torque has both magnitude and direction, making it a vector quantity.
III) Acceleration due to gravity increases with increasing depth.
Answer: False
Explanation: Acceleration due to gravity decreases with increasing depth.
IV) SI units of surface tension is Nm².
Answer: False
Explanation: The SI unit of surface tension is N/m.
V) Kinetic energy of a pendulum is maximum at the mean position.
Answer: True
Explanation: At the mean position, the speed of the pendulum is maximum, hence the kinetic energy is maximum.
Section C: Two Marks Questions
Q2. What are Dimensional constants? Give two examples.
Answer:
Dimensional constants are physical quantities that have fixed dimensions and a constant value. Examples include:
- Gravitational constant (G)
- Planck’s constant (h)
OR
Convert 1 Newton to dyne.
Answer:
1 Newton = 10⁵ dyne
Q3. A projectile is fired at an angle θ with the horizontal with a velocity u. Calculate its horizontal range.
Answer:
The horizontal range (R) of a projectile is given by:
[ R = \frac{u^2 \sin(2\theta)}{g} ]
OR
A car moving with a speed of 7 m/s accelerates and attains a speed of 27 m/s in 5 seconds. Calculate average acceleration and distance covered in 5 s.
Answer:
Average acceleration (a) = (v – u) / t = (27 m/s – 7 m/s) / 5 s = 4 m/s²
Distance covered (s) = ut + ½at² = 7 m/s * 5 s + ½ * 4 m/s² * (5 s)² = 35 m + 50 m = 85 m
Q4. What are non-conservative forces? Give an example.
Answer:
Non-conservative forces are forces where the work done depends on the path taken. An example is friction.
OR
A particle moves with a velocity ( v = (5i – 3j + 6k) ) m/s under the influence of a constant force ( F = (10i + 10j + 20k) ) N. Find instantaneous power applied to the particle.
Answer:
Power (P) = F · v = (10i + 10j + 20k) · (5i – 3j + 6k) = 50 – 30 + 120 = 140 J/s
Q5. The railway tracks have wooden or iron sleepers. Explain why?
Answer:
Sleepers are used to distribute the load of the rails and the trains over a larger area, preventing the rails from sinking into the ground. They also help in maintaining the gauge (distance between the rails).
Q6. Why is ( C_p ) greater than ( C_v )? Explain.
Answer:
( C_p ) (specific heat at constant pressure) is greater than ( C_v ) (specific heat at constant volume) because at constant pressure, some of the heat energy is used to do work in expanding the gas, whereas at constant volume, all the heat energy goes into increasing the internal energy.
Q7. Define degree of freedom.
Answer:
The degree of freedom is the number of independent ways in which a system can move or the number of independent variables required to describe the system’s state.
Q8. What do you mean by damped and forced oscillations?
Answer:
- Damped Oscillations: Oscillations where the amplitude decreases over time due to resistive forces like friction.
- Forced Oscillations: Oscillations where an external periodic force drives the system, maintaining the amplitude.
Section D: Three Marks Questions
Q9. Define and find an expression for centripetal force acting on a body moving in a circular path.
Answer:
Centripetal force is the force that keeps a body moving in a circular path and is directed towards the center. The expression is:
[ F = \frac{mv^2}{r} ]
where m is mass, v is velocity, and r is the radius of the circular path.
OR
A force of 30 kgf is just sufficient to pull a body weighing 50 kgf over a flat surface. Find the coefficient of friction & angle of friction.
Answer:
Coefficient of friction (μ) = F/R = 30 kgf / 50 kgf = 0.6
Angle of friction (α) = tan⁻¹(μ) = tan⁻¹(0.6) ≈ 31°
Q10. Derive the relation between angular momentum and Torque.
Answer:
The relation between angular momentum (L) and torque (τ) is given by:
[ \tau = \frac{dL}{dt} ]
This means torque is the rate of change of angular momentum.
Q11. Define acceleration due to gravity and find an expression for its variation with height.
Answer:
Acceleration due to gravity (g) is the acceleration of an object due to the gravitational force of the earth. The variation of g with height (h) is given by:
[ g_h = g \left(1 – \frac{2h}{R}\right) ]
where R is the radius of the earth.
OR
An artificial satellite is going around the earth close to its surface. Calculate the orbital velocity and time period. Given radius of earth = 6400 km, g = 9.8 m/s²
Answer:
Orbital velocity (v) = √(gR) = √(9.8 m/s² * 6.4 x 10⁶ m) ≈ 7.92 km/s
Time period (T) = 2π√(R/g) = 2π√(6.4 x 10⁶ m / 9.8 m/s²) ≈ 5077.6 s
Q12. Explain reversible and irreversible processes by giving suitable examples.
Answer:
- Reversible Process: A process that can be reversed without leaving any trace on the surroundings. Example: Slow compression or expansion of a gas.
- Irreversible Process: A process that cannot be reversed. Example: Burning of paper.
OR
A gram molecule of a gas at 27°C expands isothermally until its volume is doubled. Find the amount of work done. Take R=8.31 J mole⁻¹K⁻¹
Answer:
Work done (W) = 2.3026 RT log(V₂/V₁) = 2.3026 * 8.31 J/mol·K * 300 K * log(2) ≈ 1.727 x 10³ J
Q13. (a) Which type of waves do not require a material medium to propagate?
(b) What are stationary waves? Why are they so called?
Answer:
(a) Electromagnetic waves do not require a material medium to propagate.
(b) Stationary waves are formed by the superposition of two waves of the same frequency and amplitude traveling in opposite directions. They are called stationary because the positions of nodes and antinodes do not move.
Section E: Five Marks Questions
Q15. State and prove the triangular law of vector addition.
Answer:
The triangular law of vector addition states that if two vectors are represented as two sides of a triangle taken in order, then their resultant vector is represented by the third side taken in the opposite order.
Proof:
Consider two vectors A and B. To find the resultant R = A + B, place the tail of B at the head of A. The vector from the tail of A to the head of B is the resultant R.
OR
Derive the equation for the motion of a projectile fired along the horizontal.
Answer:
For a projectile fired horizontally with initial velocity u, the equations of motion are:
- Horizontal motion: x = ut
- Vertical motion: y = ½gt²
Q16. Find an expression for the height of liquid that rises in a capillary tube. What will happen if the height of the capillary tube is not sufficient?
Answer:
The height (h) of liquid rise in a capillary tube is given by:
[ h = \frac{2T \cos \theta}{\rho g r} ]
where T is surface tension, θ is the contact angle, ρ is density, g is acceleration due to gravity, and r is the radius of the tube.
If the height of the capillary tube is not sufficient, the liquid will not rise to the calculated height, and the meniscus will adjust accordingly.
OR
State and derive Bernoulli’s Theorem.
Answer:
Bernoulli’s Theorem states that for an incompressible, non-viscous fluid in steady flow, the sum of pressure energy, kinetic energy, and potential energy per unit volume remains constant.
Derivation:
Consider a fluid flowing through a pipe. By applying the work-energy principle, we get:
[ P + \frac{1}{2} \rho v^2 + \rho gh = \text{constant} ]
where P is pressure, ρ is density, v is velocity, and h is height.