Practice Questions

Q6. The relative uncertainty in the period of a satellite orbiting around the earth is 10−2 . If the relative uncertainty in the radius of the orbit is negligible, the relative uncertainty in the mass of the earth is: (1) 2 × 10−2 (2) 6 × 10−2 (3) 3 × 10−2 (4) 10−2

Q6. A force of 40 N acts on a point B at the end of an L-shaped object as shown in the figure. The angle θ that will produce the maximum moment of the force about point A is given by: (1) tan θ = 4 (2) tan θ = 14 (3) tan θ = 12 (4) tan θ = 2

Q7. A body of mass m is moving in a circular orbit of radius R about a planet of mass M . At some instant, it splits into two equal masses. The first mass moves in a circular orbit of radius R , and the other mass, in a circular 2 orbit of radius 3R . The difference between the final and initial total energies is: 2 (1) −GMm2R (2) + GMm6R (3) −GMm6R (4) GMm2R

Q7. Suppose that the angular velocity of rotation of the Earth is increased. Then, as a consequence, JEE Main 2018 (16 Apr Online) JEE Main Previous Year Paper (1) weight of the object, everywhere on the earth, will (2) weight of the object, everywhere on the earth, will decrease. increase. (3) except at poles, weight of the object on the earth, (4) there will be no change in weight anywhere on will decrease. the earth.

Q7. A body of mass m is moving in a circular orbit of radius R about a planet of mass M . At some instant, it splits into two equal masses. The first mass moves in a circular orbit of radius R . And the other mass, in a circular 2 orbit of radius 3R 2 . The difference between the final and the initial total energies is (1) + Gm6R (2) −Gm2R (3) −Gm6R (4) Gm2R

Q7. The mass of a hydrogen molecule is 3.32 × 10−27 kg. If 1023 hydrogen molecules strike, per second, a fixed wall of the area 2 cm2 at an angle of 45o to the normal, and rebound elastically with a speed of 103 m s−1, then the pressure on the wall is nearly: (1) 4.70 × 102 N m−2 (2) 2.35 × 103 N m−2 (3) 4.70 × 103 N m−2 (4) 2.35 × 102 N m−2

Q7. A thin rod MN , free to rotate in the vertical plane about the fixed end N , is held horizontal. When the end M is released the speed of this end, when the rod makes an angle α with the horizontal, will be proportional to: (see figure) (1) √cos α (2) cos α (3) sin α (4) √sin α

Q8. Take the mean distance of the moon and the sun from the earth to be 0.4 × 106 km and 150 × 106 km, respectively. Their masses are 8 × 1022 kg and 2 × 1030 kg, respectively. The radius of the earth is 6400 km. Let ΔF1 be the difference in the forces exerted by the moon at the nearest and farthest point on the earth, and ΔF2 be the difference in the forces exerted by the sun at the nearest and farthest points on the earth. Then, the number closest to ΔF1 is, ΔF2 (1) 6 (2) 10−2 (3) 2 (4) 0. 6 JEE Main 2018 (15 Apr) JEE Main Previous Year Paper

Q8. Take the mean distance of the moon and the sun from the earth to be 0.4 × 106 km and 150 × 106 km respectively. Their masses are 8 × 1022 kg and 2× 1030 kg respectively. The radius of the earth is 6400 km. Let ΔF1 be the difference in the forces exerted by the moon at the nearest and farthest points on the earth and ΔF2 be the difference in the force exerted by the sun at the nearest and farthest points on the earth. Then, the number closest to ΔF1 is: ΔF2 (1) 2 (2) 6 (3) 10−2 (4) 0.6

Q8. A thin uniform bar of length L and mass 8 m lies on a smooth horizontal table. Two point masses m and 2 m moving in the same horizontal plane from opposite sides of the bar with speeds 2v and v respectively. The masses stick to the bar after collision at a distance L and L respectively from the centre of the bar. If the bar 3 6 starts rotating about its center of mass as a result of collision, the angular speed of the bar will be: (1) v (2) 6v 6 L 5 L (3) 3v (4) v 5 L 5 L

Q8. Seven identical circular planar disks, each of mass M and radius R are welded symmetrically as shown. The moment of inertia of the arrangement about the axis normal to the plane and passing through the point P is: (1) 181 MR2 (2) 19 MR2 2 2 (3) 55 MR2 (4) 73 MR2 2 2

Q8. A small soap bubble of radius 4cm is trapped inside another bubble of radius 6cm without any contact. Let P2 be the pressure inside the inner bubble and P0 , the pressure outside the outer bubble. Radius of another bubble with pressure difference P2 −P0 between its inside and outside would be: (1) 2 .4 cm (2) 12 cm (3) 4 .8 cm (4) 6 cm

Q9. One mole of an ideal monatomic gas is taken along the path ABCA as shown in the PV diagram. The maximum temperature attained by the gas along the path BC is given by: (1) 25 P0V0 (2) 5 P0V0 4 R 8 R (3) 25 P0V0 (4) 25 P0V0 8 R 16 R

Q9. When an air bubble of radius r rises from the bottom to the surface of a lake, its radius becomes 5r . Taking the 4 atmospheric pressure to be equal to 10 m height of water column, the depth of the lake would approximately be (ignore the surface tension and the effect of temperature): (1) 10.5 m (2) 8.7 m (3) 11.2 m (4) 9.5 m

Q9. From a uniform circular disc of radius R and mass 9 M, a small disc of radius R is removed as shown in the 3 figure. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through centre of disc is: (1) 37 MR2 (2) 4MR2 9 (3) 40 MR2 (4) 10MR2 9

Q9. A thin uniform tube is bent into a circle of radius r in the vertical plane. Equal volumes of two immiscible liquids, Whose densities are ρ1 and ρ2 (ρ1 > ρ2 ), fill half the circle. The angle θ between the radius vector passing through the common interface and the vertical is: θ = (1) θ = tan−1 π2 ( ρ1−ρ2ρ1+ρ2 ) (2) tan−1[( ρ1+ρ2ρ1−ρ2 )] θ = (3) θ = tan−1 π2 ( ρ2ρ1 ) (4) tan−1π( ρ2ρ1 )

Q9. A thin uniform tube is bent into a circle of radius r in the virtical plane. Equal volumes of two immiscible liquids, whose densities are ρ1 and ρ2 (ρ1 > ρ2) fill half the circle. The angle θ between the radius vector passing through the common interface and the vertical is π (1) θ = tan−1 2 (2) θ = tan−1 π2 [ ( ρ1−ρ2ρ1+ρ2 )] ( ρ1+ρ2ρ1−ρ2 ) (3) θ = tan−1 π ρ2 ρ1 (4) θ = tan−1 π2 ρ2ρ1 ( ) ( )

Q10.A particle is moving with a uniform speed in a circular orbit of radius R in a central force inversely proportional to the nth power of R. If the period of rotation of the particle is T, then: (1) T ∝Rn/2 (2) T ∝R3/2 for any n (3) T ∝R n2 +1 (4) T ∝R n+12

Q10.One mole of an ideal monatomic gas is compressed isothermally in a rigid vessel to double its pressure at room temperature, 27oC . The magnitude of work done on the gas will be: (1) 300R (2) 300R ln 2 (3) 300 ln 6 (4) 300R ln 7

Q10.A body takes 10 minutes to cool from 60∘C to 50∘C. The temperature of surroundings is constant at 25∘C. Then, the temperature of the body after next 10 minutes will be approximately (1) 43∘C (2) 47∘C (3) 41∘C (4) 45∘C

Q10.Two moles of helium are mixed with n moles of hydrogen. If Cp = 32 for the mixture then the value of n is, Cv (1) 1 (2) 3 (3) 2 (4) 3 2

Q10.A Carnot's engine works as a refrigerator between 250 K and 300 K . It receives 500cal heat from the reservoir at the lower temperature. The amount of work done in each cycle to operate the refrigerator is: (1) 420 J (2) 2100 J (3) 772 J (4) 2520 J

Q11.An oscillator of mass M is at rest in its equilibrium position in a potential, V = 12 k(x –X)2 . A particle of mass m comes from the right with speed u and collides completely inelastic with M and sticks to it. This process repeats every time the oscillator crosses its equilibrium position. The amplitude of oscillations after 13 collisions is: (M = 10, m = 5, u = 1, k = 1) (1) 2 (2) 1 3 √3 2 (3) √35 (4) 1

Q11.Two Carnot engines A and B are operated in series. Engine A receives heat from a reservoir at 600 K and rejects heat to a reservoir at temperature T. Engine B receives heat rejected by engine A and in turn rejects it to JEE Main 2018 (15 Apr Shift 2 Online) JEE Main Previous Year Paper a reservoir at 100 K. If the efficiencies of the two engines A and B are represented by ηA and ηB respectively, then what is the value of ηA ηB (1) 12 (2) 12 7 5 (3) 5 (4) 7 12 12

Q11.A solid sphere of radius r made of a soft material of bulk modulus K is surrounded by a liquid in a cylindrical container. A massless piston of area a floats on the surface of the liquid, covering entire cross-section of JEE Main 2018 (08 Apr) JEE Main Previous Year Paper cylindrical container. When a mass m is placed on the surface of the piston to compress the liquid, the fractional decrement in the radius of the sphere ( drr ) , is: (1) mg (2) Ka Ka mg (3) Ka (4) mg 3mg 3Ka