Practice Questions

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 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. A bullet of mass 20 g has an initial speed of 1 m s-1, just before it starts penetrating a mud wall of thickness 20 cm. If the wall offers a mean resistance of 2.5 × 10-2 N, the speed of the bullet after emerging from the other side of the wall is close to: (1) 0.7 m s-1 (2) 0.3 m s-1 (3) 0.1 m s-1 (4) 0.4 m s-1

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. 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. 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 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. 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. 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 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 particle moves in one dimension from rest under the influence of a force that varies with the distance traveled by the particle as shown in the figure. The kinetic energy of the particle after it has traveled 3 m is: (1) 4 J (2) 2.5 J (3) 6.5 J (4) 5 J

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. 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 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 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 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

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. 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

Q4. A spring whose unstrentches length is l has a force constant k. The spring is cut into two pieces of unstretches lengths l1 and l2 where, l1 = nl2 and n is an integer. The ratio k1/k2 of the corresponding force constants, k1 and k2 will be: (1) 1 (2) n2 n2 (3) n (4) n1

Q4. A mass of 10 kg is suspended vertically by a rope from the roof. When a horizontal force is applied on the rope at some point, the rope deviated at an angle of 45° at the roof point. If the suspended mass is at equilibrium, the magnitude of the force applied is (g = 10 m s−2) (1) 100 N (2) 200 N (3) 140 N (4) 70 N

Q4. A particle starts from the origin at time t = 0 and moves along the positive x-axis. The graph of velocity with respect to time is shown in figure. What is the position of the particle at time t = 5s? (1) 10 m (2) 9 m (3) 6m (4) 3m → →

Q4. The position vector of the center of mass→rcm of an asymmetric uniform bar of negligible area of cross-section as shown in figure is: 13 (1)→rcm = 8 L^x + 85 Lˆy (2)→rcm = 8 5 L^x + 138 Lˆy 11 (3) →rcm = 8 3 L^x + 118 Lˆy (4)→rcm = 8 L^x + 83 Lˆy

Q4. A wedge of mass M = 4m lies on a frictionless plane. A particle of mass m approaches the wedge with speed v. There is no friction between the particle and the plane or between the particle and the wedge. The maximum height climbed by the particle on the wedge is given by: (1) v2 (2) v2 g 2g (3) 2v2 (4) 2v2 5g 7g

Q4. A body of mass 1 kg falls freely from a height of 100 m, on a platform of mass 3 kg which is mounted on a spring having spring constant k = 1.25 × 106 N/m. The bodysticks to the platform and the spring's maximum compression is found to be x. Given that g = 10 ms−2, the value of x will be close to : (1) 40 cm (2) 4 cm (3) 80 cm (4) 8 cm −−−Q5. → → → A slab is subjected to two forces F1 and F2 of same magnitude F as shown in the figure. Force F2 is in XY- plane while force F1 acts along z -axis at the point (2→i + 3→j). The moment of these forces about point O will be: (1) (3^i −2^j + 3^k) F (2) (3^i −2^j −3^k)F (3) (3^i + 2^j −3^k)F (4) (3^i + 2^j + 3^k)F