Practice Questions

Q9. A bullet of mass 5 gram, travelling with a speed of 210 m s−1 strikes a fixed wooden target. One half of its kinetic energy is converted into heat in the wood. The rise of temperature of the bullet if the specific heat of its material is 0. 030 (gram °C)−1 (1 calorie = 4 .2 ×107 ergs) close to : (1) 87. 5°C (2) 83. 3°C (3) 119. 2°C (4) 38. 4°C

Q9. To raise the temperature of a certain mass of gas by 50 °C at a constant pressure, 160 calories of heat is required. When the same mass of gas is cooled by 100°C at constant volume, 240 calories of heat is released. How many degrees of freedom does each molecule of this gas have (assume gas to be ideal)? (1) 5 (2) 6 (3) 3 (4) 7

Q9. A sound source S is moving along a straight track with speed v , and is emitting sound of frequency v0 .An observer is standing at a finite distance, at the point O, from the track. The time variation of frequency heard by observer is best represented by : (to represents the instant when the distance between the source and observer is minimum) (1) (2) (3) (4) JEE Main 2020 (06 Sep Shift 1) JEE Main Previous Year Paper

Q9. A charge Q is distributed over two concentric conducting thin spherical shells radii r and R (R > r) . If the surface charge densities on the two shells are equal, the electric potential at the common centre is : (R+r) (2R+r) 1 1 (1) Q (2) Q 2(R2+r2) (R2+r2) 4πϵ0 4πϵ0 (3) 1 (R+2r)Q (4) 1 (R+r) Q 4πϵ0 2(R2+r2) 4πϵ0 (R2+r2)

Q9. A driver in a car, approaching a vertical wall notices that the frequency of his car horn has changed from 440 Hz to 480 Hz, when it gets reflected from the wall. If the speed of sound in air is 345 m s−1, then the speed of the car is: (1) 54 km/hr (2) 36 km/hr (3) 18 km/hr (4) 24 km/hr

Q9. For a transvers wave travelling, along a straight line, the distance between two peaks (crests) is 5 m , while the distance between one crest and one trough is 1. 5 m. The possible wavelengths (in m ) of the waves are: (1) 1, 3, 5 (2) 11 , 13 , 51 , . . . . . (3) 1, 2, 3, . . . . (4) 12 , 14 , 61 , . . . . .

Q9. Two identical cylindrical vessels are kept on the ground and each contain the same liquid of density d. The area of the base of both vessels is S but the height of liquid in one vessel is x1 and in the other x2 . When both cylinders are connected through a pipe of negligible volume very close to the bottom, the liquid flows from one vessel to the other until it comes to equilibrium at a new height. The change in energy of the system in the process is : (1) gdS(x22 + x21) (2) gdS(x2 + x1)2 (3) 4 3 gdS(x2 −x1)2 (4) 41 gdS(x2 −x1)2

Q9. Two infinite planes each with uniform surface charge density +σ are kept in such a way that the angle between them is 30o . The electric field in the region shown between them is given by: (1) + 2∈0 σ [(1 √3)ˆy −ˆx2 ] (2) ∈0σ [(1 + √32 )ˆy + ˆx2 ] (3) + 2∈0 σ [(1 √3)ˆy + ˆx2 ] (4) 2∈0σ [(1 −√32 )ˆy −ˆx2 ]

Q9. Consider a mixture of n moles of helium gas and 2n moles of oxygen gas (molecules taken to be rigid) as an ideal gas. Its CP value will be: CV (1) 19 (2) 67 13 45 (3) 40 (4) 23 27 15

Q9. The plot that depicts the behavior of the mean free time τ (time between two successive collisions) for the molecules of an ideal gas, as a function of temperature (T), qualitatively, is: (Graphs are schematic and not drawn to scale) (1) (2) (3) (4)

Q9. A small spherical droplet of density d is floating exactly half immersed in a liquid of density ρ and surface tension T. The radius of the droplet is (take note that the surface tension applies an upward force on the droplet): r = (1) r = √ 3(d+ρ)g2T (2) √ (d−ρ)gT (3) T (4) 3T r = r = √ (d+ρ)g √ (2d−ρ)g

Q9. In the circuit shown in the figure, the total charge is 750 μC and the voltage across capacitor C2 is 20 V. Then the charge on capacitor C2 is : (1) 450 μC (2) 590 μC (3) 160 μC (4) 650 μC

Q10. A parallel plate capacitor has plates of area A separated by distance d between them. It is filled with a dielectric which has a dielectric constant that varies as K(x) = K0(1 + αx) where x is the distance measured from one of the plates. If (αd) << 1, the total capacitance of the system is best given by the expression: (1) AK0ε0 d (1 + αd2 ) (2) AK0ε0d [1 + ( αd2 ) 2] α2d2 (3) AK0ε0 + d (1 + αd) d (1 2 ) (4) AK0ε0 JEE Main 2020 (07 Jan Shift 1) JEE Main Previous Year Paper

Q10.Ten charges are placed on the circumference of a circle of radius R with constant angular separation between successive charges. Alternate charges 1, 3, 5, 7, 9 have charge (+q) each, while 2, 4, 6, 8, 10 have charge (–q) each. The potential V and the electric field E at the centre of the circle are respectively : (Take V = 0 at infinity) (1) V = 10q ; E = 0 (2) V = 0, E = 10q 4πϵ0R 4πϵ0R2 (3) V = 0; E = 0 (4) V = 10q ; E = 10q 4πϵ0R 4πϵ0R2

Q10.Two gases - argon (atomic radius 0.07nm, atomic weight 40 ) and xenon (atomic radius 0.1nm, atomic weight 140 ) have the same number density and are at the same temperature. The ratio of their respective mean free times is closest to: (1) 3.67 (2) 1.83 (3) 2.3 (4) 4.67

Q10.Consider a sphere of radius R which carries a uniform charge density ρ . If a sphere of radius R is carved out 2 −→ −−EA → → of it, as shown, the ratio of magnitude of electric field EA and EB , respectively, at points A and B due to− → EB the remaining portion is: (1) 21 (2) 18 34 34 (3) 17 (4) 18 54 54 + × 10−29 C m at the origin (0,0, 0) . The electric field due

Q10.A gas mixture consists of 3 moles of oxygen and 5 moles of argon at temperature T . Assuming the gases to be ideal and the oxygen bond to be rigid, the total internal energy (in units of RT ) of the mixutre is : (1) 15 (2) 13 (3) 20 (4) 11

Q10.When a particle of mass m is attached to a vertical spring of spring constant k and released, its motion, is described by y(t) = y0 sin2 ωt, where ' y' is measured from the lower end of upstretched spring. Then ω is : (1) 1 (2) 2 √gy0 √gy0 (3) √ 2y0g (4) √2gy0

Q10.A particle of mass m and charge q has an initial velocity →v= v0ˆj . If an electric field E = E0ˆi and magnetic → field B = B0ˆi act on the particle, its speed will double after a time (1) 2mv0 (2) 3mv0 qE0 qE0 (3) √3mv0 (4) √2mv0 qE0 qE0

Q10.Assume that the displacement (s) of air is proportional to the pressure difference (Δp) created by a sound wave. Displacement (s) further depends on the speed of sound (v), density of air (ρ) and the frequency (f). If Δp~10 Pa, n~300 m/s, p~1 kg/m3 f~1000Hz, then s will be of the order of (take the multiplicative constant to be 1 ) (1) 1003 mm (2) 10 mm (3) 101 mm (4) 1 mm

Q10.Two charged thin infinite plane sheets of uniform charge density σ+ and σ− , where |σ+| > |σ−|, intersect at the right angle. Which of the following best represents the electric field lines for the system: (1) (2) (3) (4)

Q10.Match the thermodynamics processes taking place in a system with the correct conditions. In the table : ΔQ is the heat supplied, ΔW is the work done and ΔU is change in internal energy of the system. Process Condition (I) Adiabatic (A) ΔW = 0 (II) Isothermal (B) ΔQ = 0 (III) Isochoric (C) ΔU ≠0, ΔW ≠0, ΔQ ≠0 (IV) Isobaric (D) ΔU = 0 (1) (I) - (A), (II) - (B), (III) - (D), (IV) - (D) (2) (I) - (B), (II) - (A), (III) - (D), (IV) - (C) (3) (I) - (A), (II) - (A), (III) - (B), (IV) - (C) (4) (I) - (B), (II) - (D), (III) - (A), (IV) - (C)

Q10.Charges Q1 and Q2 are at points A and B of a right-angled triangle OAB. The resultant electric field at point O is perpendicular to the hypotenuse, then Q1/Q2 is proportional to: (1) x31 (2) x2 x32 x1 (3) x1 (4) x22 x2 x21

Q10.A block of mass m attached to a massless spring is performing oscillatory motion of amplitude 'A' on a frictionless horizontal plane. If half of the mass of the block breaks off when it is passing through its equilibrium point, the amplitude of oscillation for the remaining system become ƒA. The value of ƒ is: (1) 1 (2) 1 √2 (3) 1 (4) √2 2

Q10.A transverse wave travels on a taut steel wire with a velocity of v when tension in it is 2.06 × 104N. When the tension is changed to T, the velocity changed to 2v . The value of T is close to: (1) 2.50 × 104N (2) 5.15 × 103 N (3) 30.5 × 104 N (4) 10.2 × 102 N