Practice Questions

Q7. A ball of mass 0.2 kg is thrown vertically upwards by applying a force by hand. If the hand moves 0.2 m which applying the force and the ball goes upto 2 m height further, find the magnitude of the force. Consider g = 10 m/s2 (1) 22 N (2) 4 N (3) 16 N (4) 20 N

Q8. The potential energy of a 1 kg particle free move along the x-axis is given by x4 V (x) = ( 4 −x22 )J The total mechanical energy of the particle 2 J. Then, the maximum speed (in m/s ) is (1) 2 (2) 3/√2 (3) √2 (4) 1/√2

Q9. A bomb of mass 16 kg at rest explodes into two pieces of masses of 4 kg and 12 kg. The velocity of the 12 kg mass is 4 ms−1 . The kinetic energy of the other mass is JEE Main 2006 JEE Main Previous Year Paper (1) 96 J (2) 144 J (3) 288 J (4) 192 J

Q10.Consider a two particle system with particles having masses m1 and m2 . If the first particle is pushed towards the centre of mass through a distance d, by what distance should the second particle be moved, so as to keep the centre of mass at the same position? (1) d (2) m2 d m1 (3) m1 d (4) m1 d m1+m2 m2

Q11.A force of −F^k acts on O, the origin of the coordinate system. The torque about the point (1, −1) (1) −F(^i −^j) (2) F(^i −^j) (3) −F(^i + ^j) (4) F(^i + ^j)

Q12.A thin circular ring of mass m and radius R is rotating about its axis with a constant angular velocity ω. Two objects each of mass M are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity ω′ = (1) ωm (2) ω(m+2M) (m+2M) m (3) ω(m−2M) (4) ωm (m+2M) (m+M)

Q13.Four point masses, each of value m, are placed at the corners of a square ABCD of side ℓ. The moment of inertia through A and parallel to BD is (1) mℓ2 (2) 2 mℓ2 (3) 3mℓ2 (4) 3 mℓ2

Q14.A wire elongates by ℓmm when a load W is hanged from it. If the wire goes over a pulley and two weights W each are hung at the two ends, the elongation of the wire will be (in mm ) (1) ℓ/2 (2) ℓ (3) 2ℓ (4) zero

Q16.Assuming the sun to be a spherical body of radius R at a temperature of TK, evaluate the total radiant power, incident on Earth, at a distance r from the Sun. (1) R2σT4 (2) 4πr20R2σT 4 r2 r2 (3) πr20R2σT 4 (4) r20R2σT 4 r2 4πr2

Q17.The work of 146 kJ is performed in order to compress one kilo mole of gas adiabatically and in this process the temperature of the gas increases by 7∘C. The gas is (R = 8.3 J mol−1 K−1) (1) monoatomic (2) diatomic (3) triatomic (4) a mixture of monoatomic and diatomic JEE Main 2006 JEE Main Previous Year Paper

Q18.Two rigid boxes containing different ideal gases are placed on a table. Box A contains one mole of nitrogen at temperature T0 , while Box B contains one mole of helium at temperature (7/3)T0 . The boxes are then put into thermal contact with each other and heat flows between them until the gases reach a common final temperature. (Ignore the heat capacity of boxes). Then, the final temperature of the gases, Tf , in terms of T0 is (1) Tf = 25 T0 (2) Tf = 37 T0 (3) Tf = 73 T0 (4) Tf = 23 T0

Q19.Starting from the origin, a body oscillates simple harmonically with a period of 2 s. After what time will its kinetic energy be 75% of the total energy? (1) 12 1 s (2) 61 s (3) 14 s (4) 13 s

Q20.The maximum velocity of a particle, executing simple harmonic motion with an amplitude 7 mm, is 4.4 m/s. The period of oscillation is (1) 100 s (2) 0.01 s (3) 10 s (4) 0.1 s

Q21.A coin is placed on a horizontal platform which undergoes vertical simple harmonic motion of angular frequency ω. The amplitude of oscillation is gradually increased. The coin will leave contact with the platform for the first time (1) at the highest position of the platform (2) at the mean position of the platform g2 (3) for an amplitude of g (4) for an amplitude of ω2 ω2

Q22.A whistle producing sound waves of frequencies 9500 Hz and above is approaching a stationary person with speed v ms−1 . The velocity of sound in air is 300 ms−1 . If the person can hear frequencies upto a maximum of 10, 000 Hz, the maximum value of v upto which he can hear the whistle is (1) 30 ms−1 (2) 15√2 ms−1 (3) 15/√2 ms−1 (4) 15 ms−1

Q23.A string is stretched between fixed points separated by 75 cm. It is observed to have resonant frequencies of 420 Hz and 315 Hz. There are no other resonant frequencies between these two. Then, the lowest resonant frequency for this string is (1) 10.5 Hz (2) 105 Hz (3) 1.05 Hz (4) 1050 Hz

Q24.A electric dipole is placed at an angle of 30∘ to a non-uniform electric field. The dipole will experience (1) a torque only (2) a translational force only in the direction of the field (3) a translational force only in a direction normal to (4) a torque as well as a translational force the direction of the field

Q25.Two insulating plates are both uniformly charged in such a way that the potential difference between them is V2 −V1 = 20 V . (i.e. plate 2 is at a higher potential). The plates are separated by d = 0.1 m and can be treated JEE Main 2006 JEE Main Previous Year Paper as infinitely large. An electron is released from rest on the inner surface of plate 1 . What is its speed when it hits plate 2? (e = 1.6 × 10−19C, me = 9.11 × 10−31 kg) (1) 32 × 10−19 m/s (2) 2.65 × 106 m/s (3) 7.02 × 1012 m/s (4) 1.87 × 106 m/s

Q26.Two spherical conductors A and B of radii 1 mm and 2 mm are separated by a distance of 5 cm and are uniformly charged. If the spheres are connected by a conducting wire then in equilibrium condition, the ratio of the magnitude of the electric fields at the surface of spheres A and B is (1) 1 : 4 (2) 4 : 1 (3) 1 : 2 (4) 2 : 1

Q27.A material ' B ' has twice the specific resistance of ' A '. A circular wire made of ' B ' has twice the diameter of a wire made of ' A '. Then for the two wires to have the same resistance, the ratio ℓA/ℓB of their respective lengths must be (1) 2 (2) 1 (3) 1 (4) 1 2 4

Q28.The Kirchhoff's first law (∑i = 0) and second law (∑iR = ∑E), where the symbols have their usual meanings, are respectively based on (1) conservation of charge, conservation of energy (2) conservation of charge, conservation of momentum (3) conservation of energy, conservation of charge (4) conservation of momentum, conservation of charge

Q29.In a Wheatstone's bridge, there resistances P, Q and R connected in the three arms and the fourth arm is formed by two resistances S1 and S2 connected in parallel. The condition for bridge to be balanced will be 2R (1) R (2) P = P = Q Q S1+S2 S1+S2 (3) (4) P = R(S1+S2) Q Q S1 S2 P = R(S1+S2)2 S1 S2 JEE Main 2006 JEE Main Previous Year Paper

Q30. The current I drawn from the 5 volt source will be (1) 0.17 A (2) 0.33 A (3) 0.5 A (4) 0.67 A

Q31.The resistance of a bulb filament is 100Ω at a temperature of 100∘C. If its temperature coefficient of resistance be 0.005 per ∘C, its resistance will become 200Ω at a temperature of (1) 200∘C (2) 300∘C (3) 400∘C (4) 500∘C

Q32.A thermocouple is made from two metals, Antimony and Bismuth. If one junction of the couple is kept hot and the other is kept cold then, an electric current will (1) flow from Antimony to Bismuth at the cold (2) flow from Antimony to Bismuth at the hot junction junction (3) flow from Bismuth to Antimony at the cold (4) not flow through the thermocouple junction