Practice Questions

Q11.The upper half of an inclined plane with inclination ϕ is perfectly smooth while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom if the coefficient of friction for the lower half is given by (1) 2 sin ϕ (2) 2 cos ϕ (3) 2 tan ϕ (4) tan ϕ

Q12.A block is kept on a frictionless inclined surface with angle of inclination α. The incline is given an acceleration a to keep the block stationary. Then a is equal to (1) g/ tan α (2) g cosec α (3) g (4) g tan α

Q13.A particle of mass 0.3 kg is subjected to a force F = −kx with k = 15 N/m. What will be its initial acceleration if it is released from a point 20 cm away from the origin? (1) 3 m/s2 (2) 15 m/s2 (3) 5 m/s2 (4) 10 m/s2

Q14.Consider a car moving on a straight road with a speed of 100 m/s. The distance at which car can be stopped is [μk = 0.5] (1) 800 m (2) 1000 m (3) 100 m (4) 400 m

Q15.An annular ring with inner and outer radii R1 and R2 is rolling without slipping with a uniform angular speed. The ratio of the forces experienced by the two particles situated on the inner and outer parts of the ring, F1/F2 is (1) R2 (2) R1 2 R1 ( R2 ) (3) 1 (4) R1 R2

Q16.A bullet fired into a fixed target loses half of its velocity after penetrating 3 cm. How much further it will penetrate before coming to rest assuming that it faces constant resistance to motion? (1) 3.0 cm (2) 2.0 cm (3) 1.5 cm (4) 1.0 cm

Q17.A spherical ball of mass 20 kg is stationary at the top of a hill of height 100 m. It rolls down a smooth surface to the ground, then climbs up another hill of height 30 m and finally rolls down to a horizontal base at a height of 20 m above the ground. The velocity attained by the ball is JEE Main 2005 JEE Main Previous Year Paper (1) 40 m/s (2) 20 m/s (3) 10 m/s (4) 10√30 m/s

Q18.A body of mass m is accelerated uniformly from rest to a speed v in a time T . The instantaneous power delivered to the body as a function time is given by (1) mv2 ⋅t (2) mv2 ⋅t2 T 2 T2 1 mv2 (3) 2 T2 ⋅t (4) 21 mv2T2 ⋅t2

Q19.A body A of mass M while falling vertically downwards under gravity breaks into two parts; a body B of mass 1/3M and a body C of mass 2/3M. The centre of mass of bodies B and C taken together shifts compared to that of body A towards (1) depends on height of breaking (2) does not shift (3) body C (4) body B

Q20.The block of mass M moving on the frictionless horizontal surface collides with a spring of spring constant K and compresses it by length L. The maximum momentum of the block after collision is (1) √MKL (2) KL2 2M (3) zero (4) ML2 K

Q21.A mass ' m ' moves with a velocity v and collides inelastically with another identical mass. After collision the 1st mass moves with velocity v/√3 in a direction perpendicular to the initial direction of motion. Find the speed of the 2nd mass after collision (1) v (2) √3v (3) 2v/√3 (4) v/√3

Q22.The moment of inertia of a uniform semicircular disc of mass M and radius r about a line perpendicular to the plane of the disc through the centre is (1) 4 1 Mr2 (2) 25 Mr2 (3) Mr2 (4) 12 Mr2

Q23.A 'T' shaped object with dimensions shown in the figure, is lying on a smooth floor. A force F is applied at the point P parallel to AB, such that the object has only the translational motion without rotation. Find the JEE Main 2005 JEE Main Previous Year Paper location of P with respect to C (1) 2 3 ℓ (2) 23 ℓ (3) 4 ℓ (4) ℓ 3

Q24.Average density of the earth (1) does not depend on g (2) is a complex function of g (3) is directly proportional to g (4) is inversely proportional to g

Q25.The change in the value of g at a height ' h ' above the surface of the earth is the same as at a depth 'd' below the surface of earth. When both ' d ' and ' h ' are much smaller than the radius of earth, then which one of the following is correct? (1) d = h2 (2) d = 32h (3) d = 2 h (4) d = h

Q26.A particle of mass 10 g is kept on the surface of a uniform sphere of mass 100 kg and radius 10 cm. Find the work to be done against the gravitational force between them to take the particle far away from the sphere (you may take G = 6.67 × 10−11Nm2/kg2 ) (1) 13.34 × 10−10 J (2) 3.33 × 10−10 J (3) 6.67 × 10−9 J (4) 6.67 × 10−10 J

Q27.If S is stress and Y is Young's modulus of material of a wire, the energy stored in the wire per unit volume is (1) 2S 2Y (2) S 2/2Y (3) 2Y /S 2 (4) S/2Y

Q28.A 20 cm long capillary tube is dipped in water. The water rises up to 8 cm. If the entire arrangement is put in a freely falling elevator the length of water column in the capillary tube will be (1) 8 cm (2) 10 cm (3) 4 cm (4) 20 cm

Q29.The figure shows a system of two concentric spheres of radii r1 and r2 and kept at temperatures T1 and T2 respectively. The radial rate of flow of heat in a substance between the two concentric sphere is proportional to JEE Main 2005 JEE Main Previous Year Paper (1) r2−r1 r1r2 (2) ln ( r1r2 ) (3) r1r2 (4) ln (r2 −r1) r2−r1

Q30.Which of the following is incorrect regarding the first law of thermodynamics? (1) It is applicable to any cyclic process (2) It is a restatement of the principle of conservation of energy (3) It introduces the concept of the internal energy (4) It introduces the concept of the entropy

Q31.The temperature-entropy diagram of a reversible engine cycle is given in the figure. Its efficiency is (1) 1/2 (2) 1/4 (3) 1/3 (4) 2/3

Q32.A system goes from A to B via two processes I and II as shown in the figure. If ΔU1 and ΔU2 are the changes in internal energies in the processes I and II respectively, the (1) ΔU1 = ΔU2 (2) relation between ΔU1 and ΔU2 can not be determined (3) ΔU2 > ΔU1 (4) ΔU2 < ΔU1

Q33.A gaseous mixture consists of 16 g of helium and 16 g of oxygen. The ratio Cp of the mixture is Cv (1) 1.59 (2) 1.62 (3) 1.4 (4) 1.54

Q34.The function sin2(ωt) represents (1) a periodic, but not simple harmonic motion with (2) a periodic, but not simple harmonic motion with a period 2π/ω a period π/ω (3) a simple harmonic motion with a period 2π/ω (4) a simple harmonic motion with a period π/ω

Q35.Two simple harmonic motions are represented by the equation y1 = 0.1 sin (100πt + π3 ) and y2 = 0.1 cos πt. The phase difference of the velocity of particle 1 w.r.t. the velocity of the particle 2 is (1) −π/6 (2) π/3 (3) −π/3 (4) π/6 JEE Main 2005 JEE Main Previous Year Paper