Practice Questions

Q12.A monoatomic gas is compressed from a volume of 2 m3 to a volume of 1 m3 at a constant pressure of 100 N m2 . Then it is heated at constant volume by supplying 150 J of energy. As a result, the internal energy of the gas (1) Decreases by 50 J (2) Increases by 250 J (3) Decreases by 250 J (4) 0 J

Q12.Two bodies of masses 1 kg and 4 kg are connected to a vertical spring, as shown in the figure. The smaller mass executes simple harmonic motion of angular frequency 25 rad s−1 , and amplitude 1. 6 cm while the bigger mass remains stationary on the ground. The maximum force exerted by the system on the floor is (take g = 10 m s−2 ). (1) 20 N (2) 60 N (3) 40 N (4) 10 N

Q12.Three rods of Copper, Brass and Steel are welded together to form a Y-shaped structure. Area of cross-section of each rod is 4 cm2 . End of copper rod is maintained at 100°C. Where as ends of brass and steel are kept at JEE Main 2014 (06 Apr) JEE Main Previous Year Paper 0°C. Lengths of the copper, brass and steel rods are 46, 13 and 12 cms respectively. The rods are thermally insulated from surroundings except at ends. Thermal conductivities of copper, brass and steel are 0. 92, 0. 26 and 0. 12 CGS units respectively. Rate of heat flow through copper rod is : (1) 1. 2 Cal /s (2) 2. 4 Cal /s (3) 4. 8 Cal /s (4) 6. 0 Cal /s

Q12.A Carnot engine absorbs 1000 J of heat energy from a reservoir at 127∘C and rejects 600 J of heat energy during each cycle. The efficiency of engine and temperature of sink will be: JEE Main 2014 (12 Apr Online) JEE Main Previous Year Paper (1) 20% and −43∘C (2) 40% and −33∘C (3) 50% and −20∘C (4) 70% and −10∘C

Q13.A gas molecule of mass M at the surface of the earth has kinetic energy equivalent to 0 °C. If it were to go up straight without colliding with any other molecules, how high it would rise? Assume that the height attained is much less than the radius of the earth. ( kB is Boltzmann constant) (1) 273kB (2) 819kB 2Mg 2Mg (3) 0 (4) 546kB3Mg

Q13.At room temperature a diatomic gas is found to have an r.m.s. speed of 1930 ms−1 . The gas is: (1) H2 (2) Cl2 (3) O2 (4) F2

Q13.One mole of diatomic ideal gas undergoes a cyclic process ABC as shown in figure. The process BC is adiabatic. The temperatures at A, B and C are 400 K, 800 K and 600 K respectively. Choose the correct statement : (1) The change in internal energy in whole cyclic (2) The change in internal energy in the process CA process is 250 R is 700 R. (3) The change in internal energy in the process AB (4) The change in internal energy in the process BC is - 350 R is - 500 R

Q13.An ideal monoatomic gas is confined in a cylinder by a spring loaded piston of cross section 8.0 × 10−3 m2 . Initially the gas is at 300 K and occupies a volume of 2.4 × 10−3 m3 and the spring is in its relaxed state as shown in figure. The gas is heated by a small heater until the piston moves out slowly by 0.1 m. The force constant of the spring is 8000 N/m and the atmospheric pressure is 1.0 × 105 N/m2 . The cylinder and the piston are thermally insulated. The piston and the spring are massless and there is no friction between the piston and the cylinder. The final temperature of the gas will be: (Neglect the heat loss through the lead wires JEE Main 2014 (11 Apr Online) JEE Main Previous Year Paper of the heater. The heat capacity of the heater coil is also negligible). (1) 300 K (2) 800 K (3) 500 K (4) 1000 K k r2 k is the spring m − 4 m2 ) where

Q13.The amplitude of a simple pendulum, oscillating in air with a small spherical bob, decreases from 10 cm to 8 cm in 40 seconds. Assuming that Stokes law is valid, and ratio of the coefficient of viscosity of air to that of carbon dioxide is 1.3, the time in which amplitude of this pendulum will reduce from 10 cm to 5 cm in carbondioxide will be close to (ln 5 = 1.601, ln 2 = 0.693). (1) 231 s (2) 142 s (3) 208 s (4) 161 s

Q14.Which of the following expressions corresponds to simple harmonic motion along a straight line, where x is the displacement and a, b, c are positive constants? (1) a + bx −cx2 (2) bx2 (3) a −bx + cx2 (4) −bx

Q14.A particle which is simultaneously subjected to two perpendicular simple harmonic motions represented by; x = a1 cos ωt and y = a2 cos 2ωt traces a curve given by : JEE Main 2014 (09 Apr Online) JEE Main Previous Year Paper (1) (2) (3) (4)

Q14.A body is in simple harmonic motion with time period T = 0.5 s and amplitude A = 1 cm. Find the average velocity in the interval in which it moves from equilibrium position to half of its amplitude. (1) 16 cm/s (2) 6 cm/s (3) 4 cm/s (4) 12 cm/s

Q14.A particle moves with simple harmonic motion in a straight line. In first τ s, after starting from rest it travels a distance a, and in next τ s it travels 2a, in same direction, then : (1) Amplitude of motion is 3a (2) Time period of oscillations is 8τ (3) Amplitude of motion is 4a (4) Time period of oscillations is 6τ

Q14.The angular frequency of the damped oscillator is given by, ω = √( constant, m is the mass of the oscillator and r is the damping constant. If the ratio mkr2 is 8%, the change in time period compared to the undamped oscillator is approximately as follows: (1) increases by 1% (2) increases by 8% (3) decreases by 1% (4) decreases by 8%

Q15.Two factories are sounding their sirens at 800 Hz. A man goes from one factory to other at a speed of 2 m/s. The velocity of sound is 320 m/s. The number of beats heard by the person in one second will be: (1) 2 (2) 4 (3) 8 (4) 10 →

Q15.A pipe of length 85 cm is closed from one end. Find the number of possible natural oscillations of air column in the pipe whose frequencies lie below 1250 Hz. The velocity of sound in air is 340 m/s. (1) 12 (2) 8 (3) 6 (4) 4 →

Q15.The total length of a sonometer wire fixed between two bridges is 110 cm. Now, two more bridges are placed to divide the length of the wire in the ratio 6 : 3 : 2 . If the tension in the wire is 400 N and the mass per unit length of the wire is 0. 01 kg m−1 , then the minimum common frequency with which all the three parts can vibrate, is (1) 1000 Hz (2) 1100 Hz (3) 100 Hz (4) 110 Hz →

Q15.A transverse wave is represented by : y = 10π sin ( 2πT t −2πλ x) For what value of the wavelength the wave velocity is twice the maximum particle velocity? (1) 40 cm (2) 60 cm (3) 10 cm (4) 20 cm

Q16.A cone of base radius R and height h is located in a uniform electric field E parallel to its base. The electric flux entering the cone is: (1) 1 EhR (2) EhR 2 (3) 2EhR (4) 4EhR

Q16.The electric field in a region of space is given by, E = E0ˆi + 2E0ˆj where E0 = 100 N C−1 . The flux of this field through a circular surface of radius 0. 02 m parallel to the Y ‐Z plane is nearly (1) 0. 02 N m2 C−1 (2) 0. 005 N m2 C−1 (3) 0. 125 N m2 C−1 (4) 3. 14 N m2 C−1

Q16.A spherically symmetric charge distribution is characterised by a charge density having the following variations: ρ(r) = ρo (1 −rR ) for r < R ρ(r) = 0 for r ≥R Where r is the distance from the centre of the charge distribution ρo is a constant. The electric field at an internal point (r < R) is: ρo (1) (2) ρ0 3 3 4εo ( r − 4Rr2 ) ε0 ( r −r24R ) (3) (4) 3 3 3εo 12εo ρo ( r − 4Rr2 ) ρo ( r − 4Rr2 )

Q16.Assume that an electric field E = 30x2ˆi exists in space. Then the potential difference VA −VO , where VO is the potential at the origin and VA the potential at x = 2 m is : (1) 120 J C−1 (2) −120 J C−1 (3) −80 J C−1 (4) 80 J C−1

Q17.A parallel plate capacitor is made of two circular plates separated by a distance of 5 mm and with a dielectric of dielectric constant 2.2 between them. When the electric field in the dielectric is 3 × 104 V/m , the charge density of the positive plate will be close to : (1) 6 × 10−7 C/m2 (2) 3 × 10−7 C/m2 (3) 3 × 104 C/m2 (4) 6 × 104 C/m2

Q17.A parallel plate capacitor is made of two plates of length 1 , width w and separated by distance d. A dielectric slab (dielectric constant K ) that fits exactly between the plates is held near the edge of the plates. It is pulled into the capacitor by a force F = −∂U∂x where U is the energy of the capacitor when dielectric is inside the capacitor up to distance x (See figure). If the charge on the capacitor is Q then the force on the dielectric when it is near the edge is: (1) Q2 d K (2) Q2 W ( K −1) 2wl2εo 2dl2ε0 (3) Q2 d (K −1) (4) Q2w K 2wl2εo 2dl2εo JEE Main 2014 (11 Apr Online) JEE Main Previous Year Paper

Q17.Three capacitances, each of 3 μF, are provided. These cannot be combined to provide the resultant capacitance of : (1) 2 μF (2) 6 μF (3) 1.5 μF (4) 1 μF