Board Boosters
The questions your board exam loves to ask
800 most-asked Class 11 & 12 (+1 / +2) questions across Physics, Chemistry, Maths and Biology — each with a model answer and the exact marking-scheme points examiners reward. Revise smart, walk in calm.
PhysicsClass 113 marksmedium
Gravitation
A satellite revolves in a circular orbit very close to the Earth's surface. Find its orbital speed. Take g = 9.8 m/s^2 and R = 6.4 x 10^6 m.
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For an orbit close to the surface the required centripetal force is provided by gravity, so v_o = sqrt(g R) = sqrt(9.8 * 6.4 x 10^6) = sqrt(6.272 x 10^7) = 7.92 x 10^3 m/s = 7.92 km/s (approximately 8 km/s).
v_o = sqrt(g R)
Marking-scheme points
- ✓v_o = sqrt(g R) for a near-surface orbit
- ✓Substitute g and R
- ✓v_o ~ 7.9 km/s
PhysicsClass 113 marksmedium
Gravitation
Show that the escape velocity from the Earth's surface is sqrt(2) times the orbital velocity of a satellite orbiting close to the surface.
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Orbital velocity near the surface: v_o = sqrt(g R). Escape velocity: v_e = sqrt(2 g R). Dividing, v_e / v_o = sqrt(2 g R) / sqrt(g R) = sqrt(2). Hence v_e = sqrt(2) * v_o (about 1.41 times).
v_e = sqrt(2) * v_o
Marking-scheme points
- ✓v_o = sqrt(gR), v_e = sqrt(2gR)
- ✓Ratio v_e/v_o = sqrt(2)
- ✓v_e = 1.41 v_o
PhysicsClass 113 marksmedium
Mechanical Properties of Solids
A wire of length 2 m and cross-sectional area 1 mm^2 stretches by 1 mm when a load of 10 N is applied. Calculate Young's modulus of the material.
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Y = (F L) / (A * delta L). Here F = 10 N, L = 2 m, A = 1 mm^2 = 1 x 10^-6 m^2, delta L = 1 mm = 1 x 10^-3 m. Y = (10 * 2) / (1 x 10^-6 * 1 x 10^-3) = 20 / (1 x 10^-9) = 2 x 10^10 N/m^2.
Y = (F L) / (A * delta L)
Marking-scheme points
- ✓Y = F L / (A delta L)
- ✓Convert mm^2 and mm to SI
- ✓Y = 2 x 10^10 N/m^2
PhysicsClass 113 marksmedium
Mechanical Properties of Fluids
What is viscosity? State Stokes' law and define terminal velocity.
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Mechanical Properties of Fluids
Calculate the total pressure at a depth of 10 m in a lake. Take atmospheric pressure = 1.0 x 10^5 Pa, density of water = 1000 kg/m^3 and g = 10 m/s^2.
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Thermal Properties of Matter
A metal rod of length 1 m is heated through 100 K. If its coefficient of linear expansion is 1.2 x 10^-5 K^-1, find the increase in its length.
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Thermal Properties of Matter
How much heat is required to melt 100 g of ice at 0 degrees C into water at 0 degrees C? The latent heat of fusion of ice is 3.36 x 10^5 J/kg.
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Thermal Properties of Matter
Name and briefly describe the three modes of heat transfer.
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Thermodynamics
Why is the molar specific heat at constant pressure (Cp) greater than that at constant volume (Cv)? State the relation between them.
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Thermodynamics
One mole of an ideal gas expands isothermally at 300 K to twice its original volume. Find the work done by the gas. Take R = 8.31 J/mol/K and ln 2 = 0.693.
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Kinetic Theory
Write the expression for the pressure exerted by an ideal gas in terms of density and mean-square speed, and hence relate pressure to the average kinetic energy per unit volume.
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Kinetic Theory
Calculate the average translational kinetic energy of a gas molecule at 300 K. Take Boltzmann constant k = 1.38 x 10^-23 J/K.
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Oscillations
Show that the total mechanical energy of a particle in SHM is constant and independent of the displacement.
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Oscillations
A particle executes SHM with amplitude 5 cm and time period 2 s. Find its maximum velocity. Take pi = 3.14.
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Waves
Write the expression for the fundamental frequency of a string of length L fixed at both ends, and explain what harmonics are.
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Waves
Define beats. Two tuning forks of frequencies 256 Hz and 260 Hz are sounded together - find the number of beats heard per second.
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Waves
A source of sound of frequency 340 Hz moves towards a stationary observer at 34 m/s. Find the apparent frequency heard. Speed of sound = 340 m/s.
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Work, Energy and Power
Derive the expression for the elastic potential energy stored in a spring stretched by x, with force constant k.
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System of Particles and Rotational Motion
Write the expression for the total kinetic energy of a body rolling without slipping, and explain its two parts.
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Units and Measurements
State any two uses and two limitations of dimensional analysis.
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