Practice Questions

Q2. In SI units, the dimensions of ϵ0 is: √ μ0 (1) AT2M-1L-1 (2) A2T3M-1L-2 (3) A-1TML3 (4) AT-3ML3 / 2

Q2. Two particles A, B are moving on two concentric circles of radii R1 and R2 with equal angular speed ω. At t = 0, their positions and direction of motion are shown in the figure: −−→ → The relative velocity VA −VB at t = 2ωπ is given by: (1) ω (R1 + R2)^i (2) −ω (R1 + R2)^i (3) ω (R2 −R1)^i (4) ω (R1 −R2)^i

Q2. Expression for time in terms of G (universal gravitational constant), h (Planck constant) and c (speed of light) is proportional to: (1) √Ghc3 (2) √hc5G (3) √Ghc5 (4) √c3Gh

Q2. The trajectory of a projectile near the surface of the earth is given as 𝑦= 2𝑥- 9𝑥2 . If it were launched at an angle θ0 with speed 𝑣0 then g = 10 m s-2: 1 5 2 3 (1) θ0 = cos-1⁡ √5 and 𝑣0 = 3 ms-1 (2) θ0 = cos-1⁡√5 and 𝑣0 = 5 ms-1 1 5 2 3 (3) θ0 = sin-1⁡ √5 and 𝑣0 = 3 ms-1 (4) θ0 = sin-1⁡√5 and 𝑣0 = 5 ms-1

Q2. A particle is moving along a circular path with a constant speed of 10 ms−1 . What is the magnitude of the change in velocity of the particle, when it moves through an angle of 60∘ around the centre of the circle? (1) 10√3 m/s (2) zero (3) 10√2 m/s (4) 10 m/s

Q2. The density of a material in SI units is 128 kg m−3. In certain units in which the unit of length is 25 cm and the unit of mass is 50g, the numerical value of density of the material is: (1) 410 (2) 16 (3) 40 (4) 640

Q2. A ball is thrown upward with an initial velocity V0 from the surface of the earth. The motion of the ball is affected by a drag force equal to mγv2 (where m is mass of the ball, v is its instantaneous velocity and γ is a constant). Time taken by the ball to rise to its zenith is: (1) 1 (2) 1 g √γg ln(1 + √γg V0) √γg tan−1(√γ V0) (3) 1 (4) 1 g g √γg sin−1(√γ V0) √2γg tan−1(√2γ V0)

Q2. A copper wire is stretched to make it 0.5% longer. The percentage change in its electrical resistance if its volume remains unchanged is: (1) 2.5% (2) 1.0% (3) 2.0% (4) 0.5%

Q2. Two vectors A and B have equal magnitudes. The magnitude of A + is ' n ' times the magnitude of ( B) → → → → A − . The angle between A and B is: ( B) n+1 ] (1) cos−1[ n2−1n2+1 ] (2) sin−1[ n−1 (3) cos−1[ n−1n+1 ] (4) sin−1[ n2−1n2+1 ]

Q2. A passenger train of length 60 m travels at a speed of 80 km / hr. Another freight train of length 120 m travels at a speed of 30 km / hr. The ratio of times taken by the passenger train to completely cross the freight train when: (i) they are moving in the same direction, and (ii) in the opposite directions is: (1) 5 (2) 3 2 2 (3) 11 (4) 25 5 11

Q3. The position vector of a particle changes with time according to the relation →r(t) = 15t2ˆi + (4 −20t2)ˆj. What is the magnitude of the acceleration at t = 1? (1) 40 (2) 25 (3) 100 (4) 50

Q3. Two particles of masses M and 2M are moving with speeds of 10 m s−1 and 5 m s−1 , as shown in the figure. They collide at the origin and after that they move along the indicated directions with speeds v1 and v2 , respectively. The values of v1 and v2 are, nearly (1) 6.5 m s−1 and 3.2 m s−1 (2) 3.2 m s−1 and 12.6 m s−1 (3) 13.02 m s−1 and 19. 7 m s−1 (4) 3.2 m s−1 and 6.3 m s−1

Q3. Two guns A and B can fire bullets at speeds 1 km/s and 2 km/s respectively. From a point on a horizontal ground, they are fired in all possible directions. The ratio of maximum areas covered by the bullets fired by the two guns, on the ground is: (1) 1 : 16 (2) 1 : 2 (3) 1 : 4 (4) 1 : 8

Q3. A particle of mass m is moving in a straight line with momentum p. Starting at time t = 0, a force F = k t acts in the same direction on the moving particle during time interval T so that its momentum changes from p to 3p. Here k is a constant. The value of T is (1) 2√kp (2) 2√pk (3) √2kp (4) √2pk

Q3. A block kept on a rough inclined plane, as shown in the figure, remains at rest upto a maximum force 2N down the inclined plane. The maximum external force up the inclined plane that does not move the block is 10N. The coefficient of static friction between the block and the plane is: [Take g = 10 m/s2 ] (1) √3 (2) 2 4 3 (3) 1 (4) √3 2 2

Q3. If Surface tension ( S ) , Moment of Inertia ( I ) and Planck's constant ( h ) , were to be taken as the fundamental units, the dimensional formula for linear momentum would be: (1) S1 / 2I1 / 2h0 (2) S1 / 2I3 / 2h-1 (3) S3 / 2I1 / 2h0 (4) S1 / 2I1 / 2h-1

Q3. A shell is fired from a fixed artillery gun with an initial speed u such that it hits the target on the ground at a distance R from it. If t1 and t2 are the values of the time taken by it to hit the target in two possible ways, the product t1t2 is: (1) R / 2g (2) R / g (3) 2R / g (4) R / 4g

Q3. Two forces P and Q, of magnitude 2F and 3F , respectively, are at an angle θ with each other. If the force Q is doubled, then their resultant also gets doubled. Then, the angle θ is: (1) 120° (2) 60° (3) 30° (4) 90°

Q3. In a car race on straight road, car A takes a time t less than car B at the finish and passes finishing point with a speed v more than that of car B. Both the cars start from rest and travel with constant acceleration a1 and a2 respectively. Then v is equal to: (1) 2a1a2 t (2) a1+a2 t a1+a2 2 (3) √a1a2t (4) √2a1a2t

Q3. A block of mass 5 kg is (i) pushed in case (A) and (ii) pulled in case (B), by a force F = 20 N, making an angle of 30o with the horizontal, as shown in the figures. The coefficient of friction between the block and floor is μ = 0.2. The difference between the accelerations of the block, in case (B) and case (A) will be: (g = 10 m s−2) (1) 3.2 m s−2 (2) 0 m s−2 (3) 0.8 m s−2 (4) 0.4 m s−2

Q3. A block of mass 10 𝑘𝑔 is kept on a rough inclined plane as shown in the figure. A force of 3 𝑁 is applied on the block. The coefficient of static friction between the plane and the block is 0.6 . What should be the minimum value of force 𝑃, such that the block does not move downward? (take 𝑔= 10 𝑚𝑠-2 ) (1) 23 𝑁 (2) 25 𝑁 (3) 18 𝑁 (4) 32 𝑁

Q3. A body is projected at t = 0 with a velocity 10 ms−1 at an angle of 60∘ with the horizontal. The radius of curvature of its trajectory at t = 1 s is R. Neglecting air resistance and taking acceleration due to gravity g = 10 ms−2 , the value of R is: (1) 10.3 m (2) 2.8 m (3) 2.5 m (4) 5.1 m

Q3. A simple pendulum, made of a string of length l and a bob of mass m, is released from a small angle θ0. It strikes a block of mass M, kept on horizontal surface at its lowest point of oscillations, elastically. It bounces back and goes up to an angle θ1. Then M is given by: (1) m( θ0−θ1θ0+θ1 ) (2) m( θ0−θ1θ0+θ1 ) (3) m θ0+θ1 (4) m θ0−θ1 2 ( θ0−θ1 ) 2 ( θ0+θ1 )

Q3. The stream of a river is flowing with a speed of 2 km h−1 . A swimmer can swim at a speed of 4 km h−1 . The direction of the swimmer with respect to the flow of the river, to cross the river straight, is (1) 150° (2) 90° (3) 120° (4) 60° part is hanging

Q3. A plane is inclined at an angle α = 30° with respect to the horizontal. A particle is projected with a speed u = 2 m s-1 , from the base of the plane, making an angle θ = 15° with respect to the plane as shown in the figure. The distance from the base, at which the particle hits the plane is close to: (Take g = 10 m s-2 ) (1) 20 cm (2) 18 cm (3) 14 cm (4) 26 cm