JEE Main Physics questions with solutions

Q1. For the equation (P + a/√(2))(V - b) = constant, what is the dimensional unit of the constant a?

1. dyne cm⁵
2. dyne cm⁴
3. dyne/cm³
4. dyne cm²

Answer: dyne cm⁴

In the van der Waals-type term a/V^2 must have the dimensions of pressure, so a = P*V^2. In CGS, P is dyne/cm^2 and V^2 is cm^6, giving a = (dyne/cm^2)*cm^6 = dyne*cm^4.

Q2. A body has a measured mass of 5.00 ± 0.05 kg and a measured volume of 1.00 ± 0.05 m³. What is the maximum possible percentage error in its density?

1. 6%
2. 3%
3. 10%
4. 5%

Answer: 6%

For density = mass/volume, the maximum fractional error adds: (dm/m)+(dV/V) = 0.05/5.00 + 0.05/1.00 = 0.01 + 0.05 = 0.06 = 6%.

Q3. A substance has a density of 4 g/cm³ in the CGS system. If a new unit system is used where the unit of length is 10 cm and the unit of mass is 100 g, what is the numerical value of the density in that system?

1. 0.4 unit
2. 40 unit
3. 400 unit
4. 0.04 unit

Answer: 40 unit

Density has dimensions M/L^3, so n2 = 4 * (1 g / 100 g) * (10 cm / 1 cm)^3 = 4 * (1/100) * 1000 = 40 units.

Q4. Which of the following physical quantities has dimensions that do not match the other three?

1. Energy density
2. Force per unit area
3. Voltage multiplied by charge, divided by volume
4. Angular momentum

Answer: Angular momentum

Energy density, force per unit area (pressure) and (voltage*charge)/volume = energy/volume all have dimensions [M L^-1 T^-2]. Angular momentum has dimensions [M L^2 T^-1], which does not match the other three.

Q5. If the percentage uncertainties in measuring mass M, length L, and time T are 1%, 1.5%, and 3% respectively, what is the percentage error in a quantity having dimensions M L⁻¹ T⁻¹?

1. 1%
2. 3.5%
3. 3%
4. 5.5%

Answer: 5.5%

The percentage error in a derived quantity can be calculated by summing the percentage uncertainties of its constituent measurements, weighted by their respective dimensions. In this case, the quantity M L⁻¹ T⁻¹ has a percentage error of 1% from mass, 1.5% from length (which is inverted, thus it contributes negatively), and 3% from time, resulting in a total of 5.5%.

Q6. What is the SI unit of the permittivity of free space, ε₀?

1. coulomb²/(newton-metre)²
2. coulomb/newton-metre
3. newton-metre²/coulomb²
4. coulomb²/newton-metre²

Answer: coulomb²/newton-metre²

Coulomb's law F = q^2/(4*pi*eps0*r^2) gives eps0 = q^2/(F r^2). The units are coulomb^2/(newton x metre^2) = C^2 N^-1 m^-2, i.e. coulomb^2/newton-metre^2.

Q7. If E, m, J and G denote energy, mass, angular momentum and the gravitational constant, respectively, then the dimensional formula of EJ²/(m⁵G²) is identical to that of which quantity?

1. angle
2. length
3. mass
4. time

Answer: angle

The dimensional formula of EJ²/(m⁵G²) simplifies to that of an angle because the units of energy, angular momentum, mass, and the gravitational constant combine in such a way that they ultimately yield a dimensionless quantity, which is characteristic of angles.

Q8. For a diode, the current–voltage relation is I = (e^(1000V/T) - 1) mA, where V is the applied voltage in volts and T is the temperature in kelvin. If the current is 5 mA at 300 K and the voltage measurement has an uncertainty of ±0.01 V, what is the resulting error in the current (in mA)?

1. 0.2 mA
2. 0.02 mA
3. 0.5 mA
4. 0.05 mA

Answer: 0.2 mA

I = e^(1000V/T)-1 = 5 mA -> e^(1000V/T) = 6. Then dI/dV = (1000/T)e^(1000V/T) = (1000/300)(6) = 20 mA/V. Error dI = 20 x 0.01 = 0.2 mA.

Q9. Which of the following has the same SI unit as impulse?

1. Energy
2. Power
3. Momentum
4. Velocity

Answer: Momentum

Impulse equals change in momentum, with SI unit N*s = kg*m/s, which is exactly the unit of momentum. Energy (J), power (W) and velocity (m/s) have different units.

Q10. A rod was found to have a measured length of 3.50 cm. Which measuring device was used for this reading?

1. A metre rule
2. A vernier caliper in which 10 vernier divisions coincide with 9 main-scale divisions, and the main scale has 10 divisions in 1 cm
3. A screw gauge with 100 circular-scale divisions and a pitch of 1 mm
4. A screw gauge with 50 circular-scale divisions and a pitch of 1 mm

Answer: A vernier caliper in which 10 vernier divisions coincide with 9 main-scale divisions, and the main scale has 10 divisions in 1 cm

A reading of 3.50 cm is given to 0.01 cm (0.1 mm). For the vernier where 10 VSD = 9 MSD and 1 MSD = 1 mm, least count = 1 MSD/10 = 0.1 mm = 0.01 cm, matching the reading. The screw gauges give 0.001 cm or 0.002 cm (three decimals), and a metre rule only 0.1 cm.

Q11. The SI unit Weber is used for measuring which of the following quantities?

1. magnetic susceptibility
2. magnetisation intensity
3. magnetic flux
4. magnetic permeability

Answer: magnetic flux

The weber (Wb = V*s = T*m^2) is the SI unit of magnetic flux.

Q12. A body is in motion inside a liquid, and the viscous resistive force on it is directly proportional to its speed. What are the dimensions of the proportionality constant?

1. [ML⁻¹T⁻¹]
2. [MLT⁻¹]
3. [M⁰LT⁻¹]
4. [ML⁰T⁻¹]

Answer: [ML⁰T⁻¹]

The proportionality constant relates the viscous force to speed, which means it must have dimensions that allow the equation to balance. Since the resistive force has dimensions of [MLT⁻²] and speed has dimensions of [LT⁻¹], the proportionality constant must have dimensions of [ML⁰T⁻¹] to ensure the units are consistent.

Q13. In a screw gauge, two complete rotations of the circular scale advance the spindle by 1 mm on the main scale, and the circular scale has 50 equal divisions. The instrument is known to have a zero error of -0.03 mm. When the diameter of a fine wire is measured, the main scale reading is 3 mm and the circular scale division coinciding with the reference line is 35. What is the wire’s diameter?

1. 3.32 mm
2. 3.73 mm
3. 3.67 mm
4. 3.38 mm

Answer: 3.38 mm

Two rotations advance 1 mm so pitch = 0.5 mm, and with 50 divisions least count = 0.5/50 = 0.01 mm. Observed reading = 3 + 35*0.01 = 3.35 mm; correcting for zero error of -0.03 mm: 3.35 - (-0.03) = 3.38 mm.

Q14. What is the SI unit used for electric flux?

1. C m⁻²
2. coulomb
3. ampere
4. volt metre

Answer: volt metre

Electric flux = E . A. Since electric field has units V/m and area m^2, flux has units (V/m)(m^2) = V m (volt metre), equivalently N m^2 C^-1. The correct unit is volt metre.

Q15. If a capacitor has capacitance C and the charge on its plate is Q, what is the dimensional formula of Q²/C?

1. [L²M²T]
2. [LMT²]
3. [L²MT⁻²]
4. [L²M²T⁻²]

Answer: [L²MT⁻²]

Energy stored in a capacitor is U = Q^2/(2C), so Q^2/C has the dimensions of energy = [M L^2 T^-2]. The correct option is [L^2 M T^-2].

Q16. What are the numbers of significant figures in 23.023, 0.0003, and 2.1 × 10⁻³, respectively?

1. 5, 1, 2
2. 5, 1, 5
3. 5, 5, 2
4. 4, 4, 2

Answer: 5, 1, 2

The number 23.023 has five significant figures because all non-zero digits and the zeros between them count. The number 0.0003 has one significant figure, as leading zeros do not count. Lastly, 2.1 × 10⁻³ has two significant figures, as only the digits in the coefficient are counted.

Q17. What are the dimensions of mobility?

1. M⁻²T²A
2. M⁻¹T²A
3. M⁻²T³A
4. M⁻¹T³A

Answer: M⁻¹T²A

The correct option reflects the relationship between mass, time, and area in the context of mobility, which is defined as the ability to move freely and is typically expressed in terms of mass per unit time and area.

Q18. Which pair of physical quantities does not share the same dimensions?

1. Torque and work
2. Momentum and Planck’s constant
3. Stress and Young’s modulus
4. Speed and (μ0ε0)⁻¹/2

Answer: Momentum and Planck’s constant

Torque and work are both M L^2 T^-2; stress and Young's modulus are both M L^-1 T^-2; speed and (mu0 eps0)^(-1/2) = c are both L T^-1. But momentum has dimensions M L T^-1 while Planck's constant has M L^2 T^-1, so this pair does not match.

Q19. In a measurement experiment, four quantities a, b, c and d have percentage errors of 1%, 2%, 3% and 4%, respectively. If a derived quantity is given by P = a³ b² / (c d), what is the percentage error in P?

1. 10%
2. 7%
3. 4%
4. 14%

Answer: 14%

For P = a^3 b^2 /(c d), %error = 3*1 + 2*2 + 1*3 + 1*4 = 3 + 4 + 3 + 4 = 14%.

Q20. In an experiment, the density of a solid sphere is to be found. Its diameter is measured using a screw gauge with pitch 0.5 mm and 50 divisions on the circular scale. The main scale reading is 2.5 mm and the circular scale reading is 20 divisions. If the measured mass of the sphere has a relative error of 2%, what is the relative percentage error in the density?

1. 0.9%
2. 2.4%
3. 3.1%
4. 4.2%

Answer: 3.1%

Least count = 0.5/50 = 0.01 mm; diameter = 2.5 + 20*0.01 = 2.7 mm with error 0.01 mm, so dd/d = 0.01/2.7 = 0.37%. Density ~ m/d^3, so error = dm/m + 3*dd/d = 2% + 3*0.37% = 2% + 1.11% = 3.1%.

Q21. A physical quantity X is defined as ε0L(ΔV/Δt), where ε0 denotes the permittivity of free space, L is a length, ΔV is a potential difference, and Δt is a time interval. The dimensional formula of X matches that of which of the following?

1. resistance
2. charge
3. potential difference
4. electric current

Answer: electric current

eps0 times a length has the dimensions of capacitance (C = eps0*Area/d ~ eps0*length). Then X = C*(dV/dt) = I, the displacement current, so X has the dimensions of electric current.

Q22. In an experiment with a simple pendulum, the largest possible error in measuring its length is 2%, while the largest possible error in measuring its time period is 3%. What is the maximum percentage error in the calculated value of acceleration due to gravity, g?

1. 5%
2. 6%
3. 1%
4. 8%

Answer: 8%

From g = 4*pi^2 L / T^2, the fractional errors add as (dg/g) = (dL/L) + 2(dT/T). So maximum % error in g = 2% + 2(3%) = 8%.

Q23. A nanocapacitor’s capacitance is expressed in a unit ‘u’ formed using the electric charge e, Bohr radius a0, Planck’s constant h, and the speed of light c. Which relation for u is correct?

1. u = e² h / a0
2. u = hc / (e² a0)
3. u = e² c / (h a0)
4. u = e² a0 / (hc)

Answer: u = e² a0 / (hc)

The correct option expresses capacitance in terms of fundamental constants, where the combination of charge, length, and constants correctly relates to the physical dimensions of capacitance, aligning with the principles of electromagnetism and quantum mechanics.

Q24. An angle-measuring device is such that 29 main-scale divisions line up exactly with 30 vernier-scale divisions. If one main-scale division equals 0.5°, what is the least count of the instrument?

1. 30 seconds
2. 1°
3. 0.5°
4. 1 minute

Answer: 1 minute

The least count is determined by the difference between one main-scale division and one vernier-scale division. Since 29 main-scale divisions equal 30 vernier divisions, the value of one vernier division is 0.5°/29, which is approximately 0.01724°. The least count, being the smallest measurable angle, is then calculated as 1 main-scale division (0.5°) minus 1 vernier division (0.01724°), resulting in a least count of 1 minute.

Q25. A thief is escaping along a straight road in a jeep traveling at 9 m/s. A policeman follows him on a motorcycle moving at 10 m/s. If the current distance between the jeep and the motorcycle is 100 m, after how much time will the policeman catch the thief?

1. 1 second
2. 19 second
3. 90 second
4. 100 second

Answer: 100 second

Closing speed = 10 - 9 = 1 m/s and the gap is 100 m, so time = 100/1 = 100 s.

Q26. A metro train begins from rest and reaches a speed of 108 km/h in 5 s. It then continues at this constant speed and finally is brought to rest by a uniform retardation over a distance of 45 m. If the entire journey covers 395 m, what is the total time taken?

1. 12.2 s
2. 15.3 s
3. 9 s
4. 17.2 s

Answer: 17.2 s

The total time taken includes the time to accelerate to 108 km/h, the time spent at constant speed, and the time to decelerate over 45 m. Calculating each segment shows that the total time sums up to 17.2 seconds, confirming the correct option.

Q27. A motor boat is moving with speed v0 when its engine is switched off. Its deceleration is described by dv/dt = −kv³, where k is a constant. The speed of the boat after time t from the moment of cut-off is

1. v0 / √((2v0²kt)+1)
2. v0 e^(−kt)
3. v0 / 2
4. v0

Answer: v0 / √((2v0²kt)+1)

dv/dt = -k v^3 gives v^-3 dv = -k dt. Integrating from v0 to v: (1/v^2 - 1/v0^2)/2 = k t, so 1/v^2 = 1/v0^2 + 2kt. Hence v = v0/sqrt(1 + 2 v0^2 k t).

Q28. From the top of a 100 m tall tower, one ball is released from rest. At the same instant, another ball is thrown straight upward from the ground with speed 25 m s^−1. How far below the top of the tower do the two balls meet?

1. 68.4 m
2. 48.4 m
3. 18.4 m
4. 78.4 m

Answer: 78.4 m

The two balls meet when they have traveled the same vertical distance. The ball dropped from the tower falls 78.4 m, leaving 21.6 m above the ground, while the ball thrown upward reaches the same height after traveling 21.6 m upward, confirming that they meet 78.4 m below the top of the tower.

Q29. A person travels 30 m due north, then 20 m due east, and finally 30√2 m in the south-west direction. What is the person's net displacement from the starting point?

1. 10 m toward the north
2. 10 m toward the south
3. 10 m toward the west
4. Zero

Answer: 10 m toward the west

North 30 -> (0,30); East 20 -> (20,30); 30sqrt2 SW = (-30,-30) -> (-10,0). Net displacement is 10 m due west.

Q30. A particle moves with velocity given by v = v0 + gt + ft². If its position is x = 0 at t = 0, what is its displacement at t = 1?

1. v0 + g/2 + f/2
2. v0 + g/2 + f/3
3. v0 + 2g + 3f
4. v0 + g + f

Answer: v0 + g/2 + f/3

x = integral_0^1 (v0 + g*t + f*t^2) dt = v0 + g/2 + f/3. The t^2 term integrates to f/3, not f/2.